TSTP Solution File: MGT032-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT032-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 : Sun Sep 18 05:22:00 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 52
% Syntax : Number of formulae : 100 ( 19 unt; 13 typ; 0 def)
% Number of atoms : 578 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 911 ( 447 ~; 417 |; 0 &)
% ( 47 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 10 >; 9 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 182 ( 165 !; 0 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
tff(greater_type,type,
greater: ( $i * $i ) > $o ).
tff(growth_rate_type,type,
growth_rate: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $i > $i ).
tff(sk1_type,type,
sk1: $i > $i ).
tff(sk2_type,type,
sk2: $i ).
tff(first_movers_type,type,
first_movers: $i ).
tff(efficient_producers_type,type,
efficient_producers: $i ).
tff(subpopulations_type,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(in_environment_type,type,
in_environment: ( $i * $i ) > $o ).
tff(stable_type,type,
stable: $i > $o ).
tff(environment_type,type,
environment: $i > $o ).
tff(selection_favors_type,type,
selection_favors: ( $i * $i * $i ) > $o ).
tff(greater_or_equal_type,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(1,plain,
( stable(sk2)
<=> stable(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
stable(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t1_5) ).
tff(3,plain,
stable(sk2),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( environment(sk2)
<=> environment(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
environment(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t1_4) ).
tff(6,plain,
environment(sk2),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [A: $i] :
refl(
( ( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) )
<=> ( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) )
<=> ! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) )
<=> ! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [A: $i] :
rewrite(
( ( ~ environment(A)
| ~ stable(A)
| in_environment(A,sk1(A)) )
<=> ( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [A: $i] :
( ~ environment(A)
| ~ stable(A)
| in_environment(A,sk1(A)) )
<=> ! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [A: $i] :
( ~ environment(A)
| ~ stable(A)
| in_environment(A,sk1(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_2) ).
tff(13,plain,
! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) )
| in_environment(sk2,sk1(sk2))
| ~ stable(sk2)
| ~ environment(sk2) )
<=> ( ~ ! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) )
| in_environment(sk2,sk1(sk2))
| ~ stable(sk2)
| ~ environment(sk2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) )
| in_environment(sk2,sk1(sk2))
| ~ stable(sk2)
| ~ environment(sk2) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [A: $i] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) )
| in_environment(sk2,sk1(sk2))
| ~ stable(sk2)
| ~ environment(sk2) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
in_environment(sk2,sk1(sk2)),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
^ [A: $i] :
refl(
( ( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) )
<=> ( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) )
<=> ! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) )
<=> ! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t1_6) ).
tff(25,plain,
! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) )
| ~ in_environment(sk2,sk1(sk2))
| subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) )
<=> ( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) )
| ~ in_environment(sk2,sk1(sk2))
| subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) )
| ~ in_environment(sk2,sk1(sk2))
| subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| subpopulations(first_movers,efficient_producers,sk2,sk3(A)) )
| ~ in_environment(sk2,sk1(sk2))
| subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))),
inference(unit_resolution,[status(thm)],[30,27,20]) ).
tff(32,plain,
^ [A: $i] :
refl(
( ( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) )
<=> ( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) )
<=> ! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) )
<=> ! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t1_8) ).
tff(36,plain,
! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) )
| ~ in_environment(sk2,sk1(sk2))
| ~ selection_favors(efficient_producers,first_movers,sk3(sk1(sk2))) )
<=> ( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) )
| ~ in_environment(sk2,sk1(sk2))
| ~ selection_favors(efficient_producers,first_movers,sk3(sk1(sk2))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) )
| ~ in_environment(sk2,sk1(sk2))
| ~ selection_favors(efficient_producers,first_movers,sk3(sk1(sk2))) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| ~ selection_favors(efficient_producers,first_movers,sk3(A)) )
| ~ in_environment(sk2,sk1(sk2))
| ~ selection_favors(efficient_producers,first_movers,sk3(sk1(sk2))) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ selection_favors(efficient_producers,first_movers,sk3(sk1(sk2))),
inference(unit_resolution,[status(thm)],[41,38,20]) ).
tff(43,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(
( ( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D)) )
<=> ( ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| selection_favors(C,B,D) )
<=> ( ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A)
| selection_favors(C,B,D) ) )),
rewrite(
( ( ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A)
| selection_favors(C,B,D) )
<=> ( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| selection_favors(C,B,D) )
<=> ( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| selection_favors(C,B,D) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| selection_favors(C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates_1) ).
tff(49,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk2)
| selection_favors(efficient_producers,first_movers,sk3(sk1(sk2)))
| ~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk2)
| selection_favors(efficient_producers,first_movers,sk3(sk1(sk2)))
| ~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( selection_favors(efficient_producers,first_movers,sk3(sk1(sk2)))
| ~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2)))
| ~ environment(sk2) )
<=> ( ~ environment(sk2)
| selection_favors(efficient_producers,first_movers,sk3(sk1(sk2)))
| ~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| selection_favors(efficient_producers,first_movers,sk3(sk1(sk2)))
| ~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2)))
| ~ environment(sk2) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk2)
| selection_favors(efficient_producers,first_movers,sk3(sk1(sk2)))
| ~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| selection_favors(efficient_producers,first_movers,sk3(sk1(sk2)))
| ~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2)))
| ~ environment(sk2) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk2)
| selection_favors(efficient_producers,first_movers,sk3(sk1(sk2)))
| ~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| selection_favors(efficient_producers,first_movers,sk3(sk1(sk2)))
| ~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2)))
| ~ environment(sk2) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk2)
| selection_favors(efficient_producers,first_movers,sk3(sk1(sk2)))
| ~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
~ greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2)))),
inference(unit_resolution,[status(thm)],[58,52,6,42,31]) ).
tff(60,plain,
^ [A: $i] :
refl(
( ( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) )
<=> ( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) )
<=> ! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) )
<=> ! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,axiom,
! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t1_7) ).
tff(64,plain,
! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) )
| ~ in_environment(sk2,sk1(sk2))
| greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) )
<=> ( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) )
| ~ in_environment(sk2,sk1(sk2))
| greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) )
| ~ in_environment(sk2,sk1(sk2))
| greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [A: $i] :
( ~ in_environment(sk2,A)
| greater_or_equal(sk3(A),A) )
| ~ in_environment(sk2,sk1(sk2))
| greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
greater_or_equal(sk3(sk1(sk2)),sk1(sk2)),
inference(unit_resolution,[status(thm)],[69,66,20]) ).
tff(71,plain,
^ [B: $i,A: $i] :
refl(
( ( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) )
<=> ( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) )
<=> ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) )
<=> ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
^ [B: $i,A: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B) )
<=> ( ~ stable(A)
| ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B) ) )),
( ( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_equal(B,sk1(A)) )
<=> ( ~ stable(A)
| ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_equal(B,sk1(A)) ) )),
rewrite(
( ( ~ stable(A)
| ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_equal(B,sk1(A)) )
<=> ( ~ stable(A)
| ~ environment(A)
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ) )),
( ( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_equal(B,sk1(A)) )
<=> ( ~ stable(A)
| ~ environment(A)
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ) )),
( ( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_equal(B,sk1(A))
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) )
<=> ( ~ stable(A)
| ~ environment(A)
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) ) )),
rewrite(
( ( ~ stable(A)
| ~ environment(A)
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) )
<=> ( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ) )),
( ( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_equal(B,sk1(A))
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) )
<=> ( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_equal(B,sk1(A))
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) )
<=> ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [B: $i,A: $i] :
( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_equal(B,sk1(A))
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_3) ).
tff(77,plain,
! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) )
| ~ stable(sk2)
| ~ environment(sk2)
| greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2)))
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) )
| ~ stable(sk2)
| ~ environment(sk2)
| greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2)))
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( ~ stable(sk2)
| ~ environment(sk2)
| greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) )
<=> ( ~ stable(sk2)
| ~ environment(sk2)
| greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2)))
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) )
| ~ stable(sk2)
| ~ environment(sk2)
| greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) )
| ~ stable(sk2)
| ~ environment(sk2)
| greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2)))
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) )
| ~ stable(sk2)
| ~ environment(sk2)
| greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) )
| ~ stable(sk2)
| ~ environment(sk2)
| greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2)))
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) )
| ~ stable(sk2)
| ~ environment(sk2)
| greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [B: $i,A: $i] :
( ~ stable(A)
| ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B) )
| ~ stable(sk2)
| ~ environment(sk2)
| greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2))))
| ~ subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2)))
| ~ greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
$false,
inference(unit_resolution,[status(thm)],[86,80,6,3,31,70,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : MGT032-2 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n002.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 : 300
% 0.12/0.33 % DateTime : Fri Sep 2 02:54:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------