%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT023-1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.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 : Tue May 5 04:47:09 PM UTC 2026
% Result : Unsatisfiable 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 23 ( 8 unt; 8 nHn; 23 RR)
% Number of literals : 72 ( 9 equ; 42 neg)
% Maximal clause size : 5 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d1_17,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| subpopulations(first_movers,efficient_producers,X1,sk1(X2,X1))
| X2 = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_17) ).
cnf(l12_20,hypothesis,
( in_environment(X1,sk2(X1))
| ~ environment(X1)
| ~ stable(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_20) ).
cnf(l12_21,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| ~ greater(growth_rate(efficient_producers,sk2(X1)),growth_rate(first_movers,sk2(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_21) ).
cnf(l12_22,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(X2,sk2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_22) ).
cnf(d1_19,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| X2 = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(growth_rate(efficient_producers,sk1(X2,X1)),growth_rate(first_movers,sk1(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_19) ).
cnf(d1_18,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| greater(sk1(X2,X1),X2)
| X2 = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_18) ).
cnf(prove_l5_25,negated_conjecture,
~ in_environment(sk3,critical_point(sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_25) ).
cnf(prove_l5_24,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_24) ).
cnf(prove_l5_23,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_23) ).
cnf(c_0_9,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| subpopulations(first_movers,efficient_producers,X1,sk1(X2,X1))
| X2 = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
d1_17 ).
cnf(c_0_10,hypothesis,
( in_environment(X1,sk2(X1))
| ~ environment(X1)
| ~ stable(X1) ),
l12_20 ).
cnf(c_0_11,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| ~ greater(growth_rate(efficient_producers,sk2(X1)),growth_rate(first_movers,sk2(X1))) ),
l12_21 ).
cnf(c_0_12,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(X2,sk2(X1)) ),
l12_22 ).
cnf(c_0_13,hypothesis,
( critical_point(X1) = sk2(X1)
| subpopulations(first_movers,efficient_producers,X1,sk1(sk2(X1),X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_14,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| X2 = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(growth_rate(efficient_producers,sk1(X2,X1)),growth_rate(first_movers,sk1(X2,X1))) ),
d1_19 ).
cnf(c_0_15,hypothesis,
( critical_point(X1) = sk2(X1)
| greater(growth_rate(efficient_producers,sk1(sk2(X1),X1)),growth_rate(first_movers,sk1(sk2(X1),X1)))
| ~ stable(X1)
| ~ greater(sk1(sk2(X1),X1),sk2(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| greater(sk1(X2,X1),X2)
| X2 = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
d1_18 ).
cnf(c_0_17,negated_conjecture,
~ in_environment(sk3,critical_point(sk3)),
prove_l5_25 ).
cnf(c_0_18,hypothesis,
( critical_point(X1) = sk2(X1)
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_10]),c_0_11]) ).
cnf(c_0_19,negated_conjecture,
stable(sk3),
prove_l5_24 ).
cnf(c_0_20,negated_conjecture,
environment(sk3),
prove_l5_23 ).
cnf(c_0_21,negated_conjecture,
~ in_environment(sk3,sk2(sk3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_22,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_10]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : MGT023-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n003.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 23:27:26 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.368s
%------------------------------------------------------------------------------