%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT027+1 : TPTP v9.2.1. Released v2.0.0.
% 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 : n016.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 : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 4 unt; 0 def)
% Number of atoms : 247 ( 11 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 337 ( 142 ~; 155 |; 28 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 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 : 94 ( 0 sgn 38 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_greater_transitivity,axiom,
! [X6,X7,X8] :
( ( greater(X6,X7)
& greater(X7,X8) )
=> greater(X6,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(l10,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] :
( greater(X2,appear(efficient_producers,X1))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X2) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10) ).
fof(mp_greater_or_equal,axiom,
! [X6,X7] :
( greater_or_equal(X6,X7)
<=> ( greater(X6,X7)
| X6 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(mp_contracts_from,axiom,
! [X1,X2] :
( ( environment(X1)
& stable(X1)
& in_environment(X1,X2)
& ! [X3] :
( ( greater(cardinality_at_time(first_movers,X3),zero)
& greater_or_equal(X3,X2) )
=> greater(zero,growth_rate(first_movers,X3)) ) )
=> contracts_from(X2,first_movers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from) ).
fof(t6,hypothesis,
! [X1,X3] :
( ( environment(X1)
& in_environment(X1,X3)
& greater_or_equal(X3,appear(efficient_producers,X1)) )
=> greater(cardinality_at_time(efficient_producers,X3),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6) ).
fof(mp_non_empty_fm_and_ep,axiom,
! [X1,X3] :
( ( environment(X1)
& in_environment(X1,X3)
& greater(cardinality_at_time(first_movers,X3),zero)
& greater(cardinality_at_time(efficient_producers,X3),zero) )
=> subpopulations(first_movers,efficient_producers,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(mp_long_stable_environments,axiom,
! [X1,X4,X5] :
( ( environment(X1)
& stable(X1)
& in_environment(X1,X4)
& greater(X5,X4) )
=> in_environment(X1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_long_stable_environments) ).
fof(mp_EP_in_stable_environments,axiom,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> in_environment(X1,appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_EP_in_stable_environments) ).
fof(prove_l9,conjecture,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] :
( greater(X2,appear(efficient_producers,X1))
& contracts_from(X2,first_movers) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9) ).
fof(c_0_9,plain,
! [X39,X40,X41] :
( ~ greater(X39,X40)
| ~ greater(X40,X41)
| greater(X39,X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_transitivity])]) ).
fof(c_0_10,hypothesis,
! [X46,X48] :
( ( greater(esk2_1(X46),appear(efficient_producers,X46))
| ~ environment(X46)
| ~ stable(X46) )
& ( ~ subpopulations(first_movers,efficient_producers,X46,X48)
| ~ greater_or_equal(X48,esk2_1(X46))
| greater(zero,growth_rate(first_movers,X48))
| ~ environment(X46)
| ~ stable(X46) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l10])])])])]) ).
fof(c_0_11,plain,
! [X42,X43] :
( ( ~ greater_or_equal(X42,X43)
| greater(X42,X43)
| X42 = X43 )
& ( ~ greater(X42,X43)
| greater_or_equal(X42,X43) )
& ( X42 != X43
| greater_or_equal(X42,X43) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_or_equal])])]) ).
fof(c_0_12,plain,
! [X30,X31] :
( ( greater(cardinality_at_time(first_movers,esk1_2(X30,X31)),zero)
| ~ environment(X30)
| ~ stable(X30)
| ~ in_environment(X30,X31)
| contracts_from(X31,first_movers) )
& ( greater_or_equal(esk1_2(X30,X31),X31)
| ~ environment(X30)
| ~ stable(X30)
| ~ in_environment(X30,X31)
| contracts_from(X31,first_movers) )
& ( ~ greater(zero,growth_rate(first_movers,esk1_2(X30,X31)))
| ~ environment(X30)
| ~ stable(X30)
| ~ in_environment(X30,X31)
| contracts_from(X31,first_movers) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_contracts_from])])])]) ).
fof(c_0_13,hypothesis,
! [X44,X45] :
( ~ environment(X44)
| ~ in_environment(X44,X45)
| ~ greater_or_equal(X45,appear(efficient_producers,X44))
| greater(cardinality_at_time(efficient_producers,X45),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6])]) ).
cnf(c_0_14,plain,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,hypothesis,
( greater(esk2_1(X1),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( greater_or_equal(esk1_2(X1,X2),X2)
| contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,hypothesis,
( greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,esk2_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( contracts_from(X2,first_movers)
| ~ greater(zero,growth_rate(first_movers,esk1_2(X1,X2)))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X33,X34] :
( ~ environment(X33)
| ~ in_environment(X33,X34)
| ~ greater(cardinality_at_time(first_movers,X34),zero)
| ~ greater(cardinality_at_time(efficient_producers,X34),zero)
| subpopulations(first_movers,efficient_producers,X33,X34) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_non_empty_fm_and_ep])]) ).
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)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,hypothesis,
( greater(X1,appear(efficient_producers,X2))
| ~ greater(X1,esk2_1(X2))
| ~ stable(X2)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_24,plain,
( esk1_2(X1,X2) = X2
| contracts_from(X2,first_movers)
| greater(esk1_2(X1,X2),X2)
| ~ in_environment(X1,X2)
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,hypothesis,
( contracts_from(esk2_1(X1),first_movers)
| ~ subpopulations(first_movers,efficient_producers,X1,esk1_2(X2,esk2_1(X1)))
| ~ in_environment(X2,esk2_1(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_19]) ).
cnf(c_0_26,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( greater(cardinality_at_time(first_movers,esk1_2(X1,X2)),zero)
| contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_28,plain,
! [X35,X36,X37] :
( ~ environment(X35)
| ~ stable(X35)
| ~ in_environment(X35,X36)
| ~ greater(X37,X36)
| in_environment(X35,X37) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_long_stable_environments])]) ).
cnf(c_0_29,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_30,hypothesis,
( esk1_2(X1,esk2_1(X2)) = esk2_1(X2)
| contracts_from(esk2_1(X2),first_movers)
| greater(esk1_2(X1,esk2_1(X2)),appear(efficient_producers,X2))
| ~ in_environment(X1,esk2_1(X2))
| ~ stable(X2)
| ~ stable(X1)
| ~ environment(X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,hypothesis,
( contracts_from(esk2_1(X1),first_movers)
| ~ greater(cardinality_at_time(efficient_producers,esk1_2(X2,esk2_1(X1))),zero)
| ~ in_environment(X1,esk1_2(X2,esk2_1(X1)))
| ~ in_environment(X2,esk2_1(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_32,plain,
( in_environment(X1,X3)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,hypothesis,
( esk1_2(X1,esk2_1(X2)) = esk2_1(X2)
| contracts_from(esk2_1(X2),first_movers)
| ~ in_environment(X2,esk1_2(X1,esk2_1(X2)))
| ~ in_environment(X1,esk2_1(X2))
| ~ stable(X2)
| ~ stable(X1)
| ~ environment(X2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_34,plain,
( esk1_2(X1,X2) = X2
| contracts_from(X2,first_movers)
| in_environment(X3,esk1_2(X1,X2))
| ~ in_environment(X3,X2)
| ~ in_environment(X1,X2)
| ~ stable(X3)
| ~ stable(X1)
| ~ environment(X3)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_35,hypothesis,
( esk1_2(X1,esk2_1(X2)) = esk2_1(X2)
| contracts_from(esk2_1(X2),first_movers)
| ~ in_environment(X1,esk2_1(X2))
| ~ in_environment(X2,esk2_1(X2))
| ~ stable(X2)
| ~ stable(X1)
| ~ environment(X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,hypothesis,
( in_environment(X1,esk2_1(X2))
| ~ in_environment(X1,appear(efficient_producers,X2))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_15]) ).
fof(c_0_37,plain,
! [X38] :
( ~ environment(X38)
| ~ stable(X38)
| in_environment(X38,appear(efficient_producers,X38)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_EP_in_stable_environments])]) ).
fof(c_0_38,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] :
( greater(X2,appear(efficient_producers,X1))
& contracts_from(X2,first_movers) ) ),
inference(assume_negation,[status(cth)],[prove_l9]) ).
cnf(c_0_39,hypothesis,
( esk1_2(X1,esk2_1(X2)) = esk2_1(X2)
| contracts_from(esk2_1(X2),first_movers)
| ~ in_environment(X1,appear(efficient_producers,X2))
| ~ in_environment(X2,esk2_1(X2))
| ~ stable(X2)
| ~ stable(X1)
| ~ environment(X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( in_environment(X1,appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,hypothesis,
( greater(cardinality_at_time(efficient_producers,esk2_1(X1)),zero)
| ~ in_environment(X1,esk2_1(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
fof(c_0_42,negated_conjecture,
! [X50] :
( environment(esk3_0)
& stable(esk3_0)
& ( ~ greater(X50,appear(efficient_producers,esk3_0))
| ~ contracts_from(X50,first_movers) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])]) ).
cnf(c_0_43,hypothesis,
( esk1_2(X1,esk2_1(X1)) = esk2_1(X1)
| contracts_from(esk2_1(X1),first_movers)
| ~ in_environment(X1,esk2_1(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,hypothesis,
( greater(cardinality_at_time(efficient_producers,esk2_1(X1)),zero)
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_36]),c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( ~ greater(X1,appear(efficient_producers,esk3_0))
| ~ contracts_from(X1,first_movers) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,negated_conjecture,
stable(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,negated_conjecture,
environment(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,hypothesis,
( contracts_from(esk2_1(X1),first_movers)
| ~ in_environment(X1,esk2_1(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_43]),c_0_44]) ).
cnf(c_0_49,negated_conjecture,
~ contracts_from(esk2_1(esk3_0),first_movers),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_15]),c_0_46]),c_0_47])]) ).
cnf(c_0_50,hypothesis,
( contracts_from(esk2_1(X1),first_movers)
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_36]),c_0_40]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_46]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : MGT027+1 : TPTP v9.2.1. Released v2.0.0.
% 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
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 23:38:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------