%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT027-1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 04:47:10 PM UTC 2026
% Result : Unsatisfiable 1.21s 1.67s
% Output : CNFRefutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 48 ( 6 unt; 13 nHn; 48 RR)
% Number of literals : 201 ( 9 equ; 140 neg)
% Maximal clause size : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mp_greater_transitivity_30,axiom,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity_30) ).
cnf(l10_35,hypothesis,
( greater(sk2(X1),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10_35) ).
cnf(mp_greater_or_equal_31,axiom,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_31) ).
cnf(mp_contracts_from_25,axiom,
( greater_or_equal(sk1(X2,X1),X2)
| contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_25) ).
cnf(l10_36,hypothesis,
( greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,sk2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10_36) ).
cnf(mp_contracts_from_26,axiom,
( contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,sk1(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_26) ).
cnf(t6_34,hypothesis,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_34) ).
cnf(mp_greater_or_equal_32,axiom,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_32) ).
cnf(mp_non_empty_fm_and_ep_27,axiom,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ greater(cardinality_at_time(efficient_producers,X2),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_27) ).
cnf(mp_contracts_from_24,axiom,
( greater(cardinality_at_time(first_movers,sk1(X2,X1)),zero)
| contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_24) ).
cnf(mp_long_stable_environments_28,axiom,
( in_environment(X1,X3)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_long_stable_environments_28) ).
cnf(mp_EP_in_stable_environments_29,axiom,
( in_environment(X1,appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_EP_in_stable_environments_29) ).
cnf(prove_l9_39,negated_conjecture,
( ~ greater(X1,appear(efficient_producers,sk3))
| ~ contracts_from(X1,first_movers) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_39) ).
cnf(prove_l9_38,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_38) ).
cnf(prove_l9_37,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_37) ).
cnf(c_0_15,axiom,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
mp_greater_transitivity_30 ).
cnf(c_0_16,hypothesis,
( greater(sk2(X1),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1) ),
l10_35 ).
cnf(c_0_17,axiom,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
mp_greater_or_equal_31 ).
cnf(c_0_18,axiom,
( greater_or_equal(sk1(X2,X1),X2)
| contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
mp_contracts_from_25 ).
cnf(c_0_19,hypothesis,
( greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,sk2(X1)) ),
l10_36 ).
cnf(c_0_20,axiom,
( contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,sk1(X2,X1))) ),
mp_contracts_from_26 ).
cnf(c_0_21,hypothesis,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1)) ),
t6_34 ).
cnf(c_0_22,axiom,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
mp_greater_or_equal_32 ).
cnf(c_0_23,hypothesis,
( greater(X1,appear(efficient_producers,X2))
| ~ greater(X1,sk2(X2))
| ~ stable(X2)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
( sk1(X1,X2) = X1
| contracts_from(X1,first_movers)
| greater(sk1(X1,X2),X1)
| ~ in_environment(X2,X1)
| ~ stable(X2)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,hypothesis,
( contracts_from(sk2(X1),first_movers)
| ~ subpopulations(first_movers,efficient_producers,X1,sk1(sk2(X1),X2))
| ~ in_environment(X2,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_20]) ).
cnf(c_0_26,axiom,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ greater(cardinality_at_time(efficient_producers,X2),zero) ),
mp_non_empty_fm_and_ep_27 ).
cnf(c_0_27,axiom,
( greater(cardinality_at_time(first_movers,sk1(X2,X1)),zero)
| contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
mp_contracts_from_24 ).
cnf(c_0_28,hypothesis,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(X1,appear(efficient_producers,X2))
| ~ in_environment(X2,X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,hypothesis,
( sk1(sk2(X1),X2) = sk2(X1)
| contracts_from(sk2(X1),first_movers)
| greater(sk1(sk2(X1),X2),appear(efficient_producers,X1))
| ~ in_environment(X2,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,hypothesis,
( contracts_from(sk2(X1),first_movers)
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(X1),X2)),zero)
| ~ in_environment(X1,sk1(sk2(X1),X2))
| ~ in_environment(X2,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_31,axiom,
( in_environment(X1,X3)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(X3,X2) ),
mp_long_stable_environments_28 ).
cnf(c_0_32,hypothesis,
( sk1(sk2(X1),X2) = sk2(X1)
| contracts_from(sk2(X1),first_movers)
| ~ in_environment(X1,sk1(sk2(X1),X2))
| ~ in_environment(X2,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_33,plain,
( sk1(X1,X2) = X1
| contracts_from(X1,first_movers)
| in_environment(X3,sk1(X1,X2))
| ~ in_environment(X3,X1)
| ~ in_environment(X2,X1)
| ~ stable(X3)
| ~ stable(X2)
| ~ environment(X3)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_34,hypothesis,
( sk1(sk2(X1),X2) = sk2(X1)
| contracts_from(sk2(X1),first_movers)
| ~ in_environment(X2,sk2(X1))
| ~ in_environment(X1,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,hypothesis,
( in_environment(X1,sk2(X2))
| ~ in_environment(X1,appear(efficient_producers,X2))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_36,hypothesis,
( sk1(sk2(X1),X2) = sk2(X1)
| contracts_from(sk2(X1),first_movers)
| ~ in_environment(X2,appear(efficient_producers,X1))
| ~ in_environment(X1,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,axiom,
( in_environment(X1,appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1) ),
mp_EP_in_stable_environments_29 ).
cnf(c_0_38,hypothesis,
( greater(cardinality_at_time(efficient_producers,sk2(X1)),zero)
| ~ in_environment(X1,sk2(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_39,hypothesis,
( sk1(sk2(X1),X1) = sk2(X1)
| contracts_from(sk2(X1),first_movers)
| ~ in_environment(X1,sk2(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,hypothesis,
( greater(cardinality_at_time(efficient_producers,sk2(X1)),zero)
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_35]),c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( ~ greater(X1,appear(efficient_producers,sk3))
| ~ contracts_from(X1,first_movers) ),
prove_l9_39 ).
cnf(c_0_42,negated_conjecture,
stable(sk3),
prove_l9_38 ).
cnf(c_0_43,negated_conjecture,
environment(sk3),
prove_l9_37 ).
cnf(c_0_44,hypothesis,
( contracts_from(sk2(X1),first_movers)
| ~ in_environment(X1,sk2(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_39]),c_0_40]) ).
cnf(c_0_45,negated_conjecture,
~ contracts_from(sk2(sk3),first_movers),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_16]),c_0_42]),c_0_43])]) ).
cnf(c_0_46,hypothesis,
( contracts_from(sk2(X1),first_movers)
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_37]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_42]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : MGT027-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.10/0.29 % Computer : n018.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon May 4 23:27:47 EDT 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.30 % start to proof: theBenchmark
% 1.21/1.67 % Version : CSE_E---1.7
% 1.21/1.67 % Problem : theBenchmark.p
% 1.21/1.67 % SZS status Unsatisfiable for theBenchmark.p
% 1.21/1.67 % SZS output start CNFRefutation
% See solution above
% 1.21/1.67 % Total time : 1.368s
%------------------------------------------------------------------------------