%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 : Fri Sep 25 02:11:33 PM UTC 2026
% Result : Theorem 5.32s 1.17s
% Output : Proof 5.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 92 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 34 ~; 28 |; 21 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 50 ( 0 sgn 24 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,hypothesis,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
fof(f1_nnf,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,To) )
| ~ stable(E)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,T] :
( ( ( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,sk0(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,sk0(E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c1,plain,
( in_environment(X0,sk0(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(environment(X0),true,ifeq(stable(X0),true,in_environment(X0,sk0(X0)),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
fof(f2,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> selection_favors(efficient_producers,first_movers,T) )
& in_environment(E,To) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t1) ).
fof(f2_neg,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> selection_favors(efficient_producers,first_movers,T) )
& in_environment(E,To) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
? [E] :
( ! [To] :
( ? [T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To) )
& stable(E)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
! [To] :
( ( ( ~ selection_favors(efficient_producers,first_movers,sk2(To))
& greater_or_equal(sk2(To),To)
& subpopulations(first_movers,efficient_producers,sk1,sk2(To)) )
| ~ in_environment(sk1,To) )
& stable(sk1)
& environment(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f2_nnf]) ).
cnf(c3,plain,
environment(sk1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi3,negated_conjecture,
environment(sk1) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(c4,plain,
stable(sk1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi4,negated_conjecture,
stable(sk1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h0,plain,
in_environment(sk1,sk0(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi3,hi4]) ).
cnf(c6,plain,
( greater_or_equal(sk2(X1),X1)
| ~ in_environment(sk1,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi6,negated_conjecture,
ifeq(in_environment(sk1,X0),true,greater_or_equal(sk2(X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h1,plain,
greater_or_equal(sk2(sk0(sk1)),sk0(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h0]) ).
cnf(c5,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2(X1))
| ~ in_environment(sk1,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi5,negated_conjecture,
ifeq(in_environment(sk1,X0),true,subpopulations(first_movers,efficient_producers,sk1,sk2(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h2,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2(sk0(sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi5,h0]) ).
cnf(c2,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi2,axiom,
ifeq(environment(X0),true,ifeq(stable(X0),true,ifeq(subpopulations(first_movers,efficient_producers,X0,X1),true,ifeq(greater_or_equal(X1,sk0(X0)),true,greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h3,plain,
greater(growth_rate(efficient_producers,sk2(sk0(sk1))),growth_rate(first_movers,sk2(sk0(sk1)))) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi3,hi4,h2,h1]) ).
fof(f0,axiom,
! [E,S1,S2,T] :
( ( greater(growth_rate(S2,T),growth_rate(S1,T))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> selection_favors(S2,S1,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f0_nnf,plain,
! [E,S1,S2,T] :
( selection_favors(S2,S1,T)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,S1,S2,T] :
( selection_favors(S2,S1,T)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(environment(X0),true,ifeq(subpopulations(X1,X2,X0,X3),true,ifeq(greater(growth_rate(X2,X3),growth_rate(X1,X3)),true,selection_favors(X2,X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h4,plain,
selection_favors(efficient_producers,first_movers,sk2(sk0(sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h2,h3]) ).
cnf(c7,plain,
( ~ selection_favors(efficient_producers,first_movers,sk2(X1))
| ~ in_environment(sk1,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi7,negated_conjecture,
ifeq(in_environment(sk1,X0),true,ifeq(selection_favors(efficient_producers,first_movers,sk2(X0)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi7,h0,h4]) ).
cnf(t44,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t44]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 01:06:14 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.32/1.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.32/1.17 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------