%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT036+3 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 02:11:45 PM UTC 2026
% Result : Theorem 6.09s 1.18s
% Output : Proof 6.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 18 unt; 0 def)
% Number of atoms : 83 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 81 ( 32 ~; 26 |; 20 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 56 ( 0 sgn 28 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [E,S1,S2,T] :
( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> subpopulations(S2,S1,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f0_nnf,plain,
! [E,S1,S2,T] :
( subpopulations(S2,S1,E,T)
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,S1,S2,T] :
( subpopulations(S2,S1,E,T)
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( subpopulations(X2,X1,X0,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,subpopulations(X2,X1,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f2,hypothesis,
? [E,T] :
( greater(zero,growth_rate(efficient_producers,T))
& greater_or_equal(growth_rate(first_movers,T),zero)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star) ).
fof(f2_nnf,plain,
? [E,T] :
( greater(zero,growth_rate(efficient_producers,T))
& greater_or_equal(growth_rate(first_movers,T),zero)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( greater(zero,growth_rate(efficient_producers,sk1))
& greater_or_equal(growth_rate(first_movers,sk1),zero)
& subpopulations(first_movers,efficient_producers,sk0,sk1)
& environment(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f2_nnf]) ).
cnf(c4,plain,
environment(sk0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi4,axiom,
environment(sk0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(c5,plain,
subpopulations(first_movers,efficient_producers,sk0,sk1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi5,axiom,
subpopulations(first_movers,efficient_producers,sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h0,plain,
subpopulations(efficient_producers,first_movers,sk0,sk1) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi4,hi5]) ).
fof(f1,hypothesis,
! [E,S1,S2,T] :
( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) )
<=> outcompetes(S2,S1,T) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(f1_nnf,plain,
! [E,S1,S2,T] :
( ( ( ~ outcompetes(S2,S1,T)
| ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) ) )
& ( outcompetes(S2,S1,T)
| ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero) ) )
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,S1,S2,T] :
( ( ( ~ outcompetes(S2,S1,T)
| ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) ) )
& ( outcompetes(S2,S1,T)
| ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero) ) )
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( outcompetes(X2,X1,X3)
| ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(environment(X0),true,ifeq(subpopulations(X1,X2,X0,X3),true,ifeq(greater_or_equal(growth_rate(X2,X3),zero),true,ifeq(greater(zero,growth_rate(X1,X3)),true,outcompetes(X2,X1,X3),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c6,plain,
greater_or_equal(growth_rate(first_movers,sk1),zero),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi6,axiom,
greater_or_equal(growth_rate(first_movers,sk1),zero) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(c7,plain,
greater(zero,growth_rate(efficient_producers,sk1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi7,axiom,
greater(zero,growth_rate(efficient_producers,sk1)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h1,plain,
outcompetes(first_movers,efficient_producers,sk1) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi4,h0,hi6,hi7]) ).
fof(f3,conjecture,
? [E,T] :
( outcompetes(first_movers,efficient_producers,T)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_star) ).
fof(f3_neg,negated_conjecture,
~ ? [E,T] :
( outcompetes(first_movers,efficient_producers,T)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
! [E,T] :
( ~ outcompetes(first_movers,efficient_producers,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
! [E,T] :
( ~ outcompetes(first_movers,efficient_producers,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c8,plain,
( ~ outcompetes(first_movers,efficient_producers,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(environment(X0),true,ifeq(subpopulations(first_movers,efficient_producers,X0,X1),true,ifeq(outcompetes(first_movers,efficient_producers,X1),true,false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi8,hi4,hi5,h1]) ).
cnf(t49,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t49]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+3 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 01:10:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.09/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.09/1.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------