TSTP Solution File: MGT036-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT036-1 : 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 05:22:04 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 61
% Syntax : Number of formulae : 121 ( 26 unt; 13 typ; 0 def)
% Number of atoms : 783 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 1241 ( 602 ~; 575 |; 0 &)
% ( 64 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 36 ( 36 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 8 >; 9 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 362 ( 326 !; 0 ?; 362 :)
% Comments :
%------------------------------------------------------------------------------
tff(greater_or_equal_type,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(zero_type,type,
zero: $i ).
tff(growth_rate_type,type,
growth_rate: ( $i * $i ) > $i ).
tff(sk2_type,type,
sk2: $i ).
tff(first_movers_type,type,
first_movers: $i ).
tff(subpopulations_type,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $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(in_environment_type,type,
in_environment: ( $i * $i ) > $o ).
tff(resilience_type,type,
resilience: $i > $i ).
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/sandbox2/benchmark/theBenchmark.p',prove_t5_13) ).
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/sandbox2/benchmark/theBenchmark.p',prove_t5_12) ).
tff(6,plain,
environment(sk1),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [B: $i,A: $i] :
refl(
( ( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
<=> ( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
<=> ! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
<=> ! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| subpopulations(efficient_producers,first_movers,A,B) )
<=> ( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| subpopulations(efficient_producers,first_movers,A,B) )
<=> ! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| subpopulations(efficient_producers,first_movers,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_FM_and_EP_1) ).
tff(13,plain,
! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2) )
<=> ( ~ ! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ 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,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ ! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ 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,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) )
| subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ ! [B: $i,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ 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,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ 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,A: $i] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ 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,
( outcompetes(first_movers,efficient_producers,sk2)
<=> outcompetes(first_movers,efficient_producers,sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
outcompetes(first_movers,efficient_producers,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_14) ).
tff(26,plain,
outcompetes(first_movers,efficient_producers,sk2),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(
( ( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ outcompetes(C,B,D) )
<=> ( ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero) )
<=> ( ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A)
| greater_or_equal(growth_rate(C,D),zero) ) )),
rewrite(
( ( ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A)
| greater_or_equal(growth_rate(C,D),zero) )
<=> ( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero) )
<=> ( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_8) ).
tff(33,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk1)
| greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk1)
| greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( ~ outcompetes(first_movers,efficient_producers,sk2)
| greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ environment(sk1)
| greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk1)
| greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk1)
| greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk1)
| greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
greater_or_equal(growth_rate(first_movers,sk2),zero),
inference(unit_resolution,[status(thm)],[42,36,6,26,23]) ).
tff(44,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(
( ( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ outcompetes(C,B,D) )
<=> ( ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D)) )
<=> ( ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A)
| greater(zero,growth_rate(B,D)) ) )),
rewrite(
( ( ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A)
| greater(zero,growth_rate(B,D)) )
<=> ( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
( ( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D)) )
<=> ( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_9) ).
tff(50,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk1)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk1)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ environment(sk1)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk1)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk1)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) )
| ~ environment(sk1)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(unit_resolution,[status(thm)],[59,53,6,26,23]) ).
tff(61,plain,
^ [B: $i,A: $i] :
refl(
( ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) )
<=> ( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) )
<=> ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [B: $i,A: $i] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur_2) ).
tff(67,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| in_environment(sk1,sk2) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| in_environment(sk1,sk2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| in_environment(sk1,sk2) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [B: $i,A: $i] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A)
| in_environment(A,B) )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| in_environment(sk1,sk2) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
in_environment(sk1,sk2),
inference(unit_resolution,[status(thm)],[73,70,6,3]) ).
tff(75,plain,
( greater(resilience(efficient_producers),resilience(first_movers))
<=> greater(resilience(efficient_producers),resilience(first_movers)) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2_11) ).
tff(77,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(
( ( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) )
<=> ( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ environment(A)
| ~ in_environment(A,B)
| greater(zero,growth_rate(C,B)) )
<=> ( ~ environment(A)
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| greater(zero,growth_rate(C,B))
| ~ greater(resilience(D),resilience(C)) )
<=> ( ~ environment(A)
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ greater(resilience(D),resilience(C)) ) )),
rewrite(
( ( ~ environment(A)
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ greater(resilience(D),resilience(C)) )
<=> ( ~ environment(A)
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| greater(zero,growth_rate(C,B))
| ~ greater(resilience(D),resilience(C)) )
<=> ( ~ environment(A)
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| greater(zero,growth_rate(C,B))
| ~ greater(resilience(D),resilience(C))
| ~ greater(zero,growth_rate(D,B)) )
<=> ( ~ environment(A)
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ greater(zero,growth_rate(D,B)) ) )),
rewrite(
( ( ~ environment(A)
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ greater(zero,growth_rate(D,B)) )
<=> ( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ) )),
( ( ~ environment(A)
| ~ in_environment(A,B)
| greater(zero,growth_rate(C,B))
| ~ greater(resilience(D),resilience(C))
| ~ greater(zero,growth_rate(D,B)) )
<=> ( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ in_environment(A,B)
| greater(zero,growth_rate(C,B))
| ~ greater(resilience(D),resilience(C))
| ~ greater(zero,growth_rate(D,B)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ in_environment(A,B)
| greater(zero,growth_rate(C,B))
| ~ greater(resilience(D),resilience(C))
| ~ greater(zero,growth_rate(D,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12_10) ).
tff(84,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) )
| greater(zero,growth_rate(first_movers,sk2))
| ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ in_environment(sk1,sk2) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) )
| greater(zero,growth_rate(first_movers,sk2))
| ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ in_environment(sk1,sk2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| greater(zero,growth_rate(first_movers,sk2))
| ~ in_environment(sk1,sk2) )
<=> ( greater(zero,growth_rate(first_movers,sk2))
| ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ in_environment(sk1,sk2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) )
| ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| greater(zero,growth_rate(first_movers,sk2))
| ~ in_environment(sk1,sk2) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) )
| greater(zero,growth_rate(first_movers,sk2))
| ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ in_environment(sk1,sk2) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) )
| ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| greater(zero,growth_rate(first_movers,sk2))
| ~ in_environment(sk1,sk2) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) )
| greater(zero,growth_rate(first_movers,sk2))
| ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ in_environment(sk1,sk2) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) )
| ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| greater(zero,growth_rate(first_movers,sk2))
| ~ in_environment(sk1,sk2) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ environment(A)
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) )
| greater(zero,growth_rate(first_movers,sk2))
| ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ in_environment(sk1,sk2) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
greater(zero,growth_rate(first_movers,sk2)),
inference(unit_resolution,[status(thm)],[93,87,77,6,74,60]) ).
tff(95,plain,
^ [B: $i,A: $i] :
refl(
( ( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) )
<=> ( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) )
<=> ! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) )
<=> ! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
^ [B: $i,A: $i] :
rewrite(
( ( ~ greater_or_equal(growth_rate(A,B),zero)
| ~ greater(zero,growth_rate(A,B)) )
<=> ( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [B: $i,A: $i] :
( ~ greater_or_equal(growth_rate(A,B),zero)
| ~ greater(zero,growth_rate(A,B)) )
<=> ! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,axiom,
! [B: $i,A: $i] :
( ~ greater_or_equal(growth_rate(A,B),zero)
| ~ greater(zero,growth_rate(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_5) ).
tff(101,plain,
! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ),
inference(modus_ponens,[status(thm)],[103,96]) ).
tff(105,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) )
| ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) )
| ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ~ ! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) )
| ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [B: $i,A: $i] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) )
| ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
$false,
inference(unit_resolution,[status(thm)],[107,104,94,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : MGT036-1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 02:58:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------