%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT036-3 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n031.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 06:24:03 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 28
% Syntax : Number of formulae : 60 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 414 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 670 ( 334 ~; 302 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 202 ( 182 !; 0 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
tff(subpopulations_type,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(first_movers_type,type,
first_movers: $i ).
tff(efficient_producers_type,type,
efficient_producers: $i ).
tff(environment_type,type,
environment: $i > $o ).
tff(outcompetes_type,type,
outcompetes: ( $i * $i * $i ) > $o ).
tff(greater_type,type,
greater: ( $i * $i ) > $o ).
tff(growth_rate_type,type,
growth_rate: ( $i * $i ) > $i ).
tff(zero_type,type,
zero: $i ).
tff(greater_or_equal_type,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(1,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
<=> subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_6) ).
tff(3,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( environment(sk1)
<=> environment(sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_5) ).
tff(6,plain,
environment(sk1),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
rewrite(( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| subpopulations(C,B,A,D) )
<=> ( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| subpopulations(C,B,A,D) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| subpopulations(C,B,A,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).
tff(13,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
^ [B: $i,A: $i] :
refl(( ( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
<=> ( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
<=> ! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
<=> ! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [B: $i,A: $i] :
rewrite(( ( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ outcompetes(first_movers,efficient_producers,B) )
<=> ( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ outcompetes(first_movers,efficient_producers,B) )
<=> ! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ outcompetes(first_movers,efficient_producers,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_star_9) ).
tff(30,plain,
! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i] :
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
~ outcompetes(first_movers,efficient_producers,sk2),
inference(unit_resolution,[status(thm)],[36,6,3,33]) ).
tff(38,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
<=> greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
greater(zero,growth_rate(efficient_producers,sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_8) ).
tff(40,plain,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( greater_or_equal(growth_rate(first_movers,sk2),zero)
<=> greater_or_equal(growth_rate(first_movers,sk2),zero) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
greater_or_equal(growth_rate(first_movers,sk2),zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_7) ).
tff(43,plain,
greater_or_equal(growth_rate(first_movers,sk2),zero),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) )
<=> ( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater_or_equal(growth_rate(C,D),zero) )
<=> ( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| ~ greater_or_equal(growth_rate(C,D),zero) ) )),
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ greater(zero,growth_rate(B,D)) )
<=> ( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ greater(zero,growth_rate(B,D)) ) )),
rewrite(( ( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ greater(zero,growth_rate(B,D)) )
<=> ( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ) )),
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ greater(zero,growth_rate(B,D)) )
<=> ( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ) )),
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ greater(zero,growth_rate(B,D))
| outcompetes(C,B,D) )
<=> ( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero)
| outcompetes(C,B,D) ) )),
rewrite(( ( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero)
| outcompetes(C,B,D) )
<=> ( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ) )),
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ greater(zero,growth_rate(B,D))
| outcompetes(C,B,D) )
<=> ( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ greater(zero,growth_rate(B,D))
| outcompetes(C,B,D) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ greater(zero,growth_rate(B,D))
| outcompetes(C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_2) ).
tff(50,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) )
| outcompetes(first_movers,efficient_producers,sk2)
| ~ environment(sk1)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) )
| outcompetes(first_movers,efficient_producers,sk2)
| ~ environment(sk1)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1)
| outcompetes(first_movers,efficient_producers,sk2)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) )
<=> ( outcompetes(first_movers,efficient_producers,sk2)
| ~ environment(sk1)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) )
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1)
| outcompetes(first_movers,efficient_producers,sk2)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) )
| outcompetes(first_movers,efficient_producers,sk2)
| ~ environment(sk1)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) )
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1)
| outcompetes(first_movers,efficient_producers,sk2)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) )
| outcompetes(first_movers,efficient_producers,sk2)
| ~ environment(sk1)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) )
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1)
| outcompetes(first_movers,efficient_producers,sk2)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A)
| outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero) )
| outcompetes(first_movers,efficient_producers,sk2)
| ~ environment(sk1)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
$false,
inference(unit_resolution,[status(thm)],[59,53,6,43,40,37,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036-3 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.06/0.33 % Computer : n031.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Mon Sep 7 12:45:43 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------