%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT020+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 : n026.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 04:47:08 PM UTC 2026
% Result : Theorem 1.26s 1.73s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 5 unt; 0 def)
% Number of atoms : 148 ( 9 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 172 ( 68 ~; 68 |; 20 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_positive_function_difference,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& greater_or_equal(X2,X3)
& greater_or_equal(X4,X2)
& subpopulations(first_movers,efficient_producers,X1,X4)
& greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) )
=> ( ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
=> greater(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_function_difference) ).
fof(mp_times_in_order,axiom,
! [X1,X3,X4] :
( ( environment(X1)
& greater_or_equal(X3,start_time(X1))
& greater(X4,X3)
& in_environment(X1,X4) )
=> in_environment(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_times_in_order) ).
fof(mp_initial_time,axiom,
! [X1] :
( environment(X1)
=> greater_or_equal(initial_FM_EP(X1),start_time(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_initial_time) ).
fof(mp_greater_or_equal,axiom,
! [X5,X6] :
( greater_or_equal(X5,X6)
=> ( greater(X5,X6)
| X5 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(mp_earliest_time_point,axiom,
! [X1,X2] :
( environment(X1)
=> ( ( in_environment(X1,initial_FM_EP(X1))
=> subpopulations(first_movers,efficient_producers,X1,initial_FM_EP(X1)) )
& ( subpopulations(first_movers,efficient_producers,X1,X2)
=> greater_or_equal(X2,initial_FM_EP(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_point) ).
fof(a8,hypothesis,
! [X1] :
( environment(X1)
=> greater(disbanding_rate(first_movers,initial_FM_EP(X1)),disbanding_rate(efficient_producers,initial_FM_EP(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8) ).
fof(prove_l2,conjecture,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2) ).
fof(mp_time_point_occurs,axiom,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occurs) ).
fof(l3,axiom,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
fof(c_0_9,plain,
! [X1,X2,X3,X4] :
( ( environment(X1)
& greater_or_equal(X2,X3)
& greater_or_equal(X4,X2)
& subpopulations(first_movers,efficient_producers,X1,X4)
& greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) )
=> ( ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
=> greater(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4)) ) ),
inference(fof_simplification,[status(thm)],[mp_positive_function_difference]) ).
fof(c_0_10,plain,
! [X45,X46,X47] :
( ~ environment(X45)
| ~ greater_or_equal(X46,start_time(X45))
| ~ greater(X47,X46)
| ~ in_environment(X45,X47)
| in_environment(X45,X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_times_in_order])]) ).
fof(c_0_11,plain,
! [X44] :
( ~ environment(X44)
| greater_or_equal(initial_FM_EP(X44),start_time(X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_initial_time])]) ).
fof(c_0_12,plain,
! [X51,X52] :
( ~ greater_or_equal(X51,X52)
| greater(X51,X52)
| X51 = X52 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_or_equal])]) ).
fof(c_0_13,plain,
! [X36,X37] :
( ( ~ in_environment(X36,initial_FM_EP(X36))
| subpopulations(first_movers,efficient_producers,X36,initial_FM_EP(X36))
| ~ environment(X36) )
& ( ~ subpopulations(first_movers,efficient_producers,X36,X37)
| greater_or_equal(X37,initial_FM_EP(X36))
| ~ environment(X36) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_earliest_time_point])])]) ).
fof(c_0_14,plain,
! [X38,X39,X40,X41] :
( ~ environment(X38)
| ~ greater_or_equal(X39,X40)
| ~ greater_or_equal(X41,X39)
| ~ subpopulations(first_movers,efficient_producers,X38,X41)
| ~ greater(disbanding_rate(first_movers,X40),disbanding_rate(efficient_producers,X40))
| decreases(difference(disbanding_rate(first_movers,X39),disbanding_rate(efficient_producers,X39)))
| greater(disbanding_rate(first_movers,X41),disbanding_rate(efficient_producers,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
fof(c_0_15,hypothesis,
! [X53] :
( ~ environment(X53)
| greater(disbanding_rate(first_movers,initial_FM_EP(X53)),disbanding_rate(efficient_producers,initial_FM_EP(X53))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a8])]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)) ),
inference(assume_negation,[status(cth)],[prove_l2]) ).
cnf(c_0_17,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ greater_or_equal(X2,start_time(X1))
| ~ greater(X3,X2)
| ~ in_environment(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( greater_or_equal(initial_FM_EP(X1),start_time(X1))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( greater_or_equal(X2,initial_FM_EP(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_21,plain,
! [X42,X43] :
( ~ environment(X42)
| ~ subpopulations(first_movers,efficient_producers,X42,X43)
| in_environment(X42,X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_point_occurs])]) ).
cnf(c_0_22,plain,
( decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
| greater(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4))
| ~ environment(X1)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X4,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X4)
| ~ greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
( greater(disbanding_rate(first_movers,initial_FM_EP(X1)),disbanding_rate(efficient_producers,initial_FM_EP(X1)))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_24,negated_conjecture,
( environment(esk1_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& ~ greater(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_25,plain,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
inference(fof_simplification,[status(thm)],[l3]) ).
cnf(c_0_26,plain,
( in_environment(X1,initial_FM_EP(X1))
| ~ greater(X2,initial_FM_EP(X1))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_27,plain,
( X1 = initial_FM_EP(X2)
| greater(X1,initial_FM_EP(X2))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
( greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))
| decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
| ~ greater_or_equal(X2,initial_FM_EP(X3))
| ~ greater_or_equal(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X4,X1)
| ~ environment(X4)
| ~ environment(X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
~ greater(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_33,plain,
! [X34,X35] :
( ~ environment(X34)
| ~ subpopulations(first_movers,efficient_producers,X34,X35)
| ~ decreases(difference(disbanding_rate(first_movers,X35),disbanding_rate(efficient_producers,X35))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
cnf(c_0_34,plain,
( X1 = initial_FM_EP(X2)
| in_environment(X2,initial_FM_EP(X2))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ greater_or_equal(X1,initial_FM_EP(X2))
| ~ greater_or_equal(esk2_0,X1)
| ~ environment(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_36,plain,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( subpopulations(first_movers,efficient_producers,X1,initial_FM_EP(X1))
| ~ in_environment(X1,initial_FM_EP(X1))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_38,negated_conjecture,
( initial_FM_EP(esk1_0) = esk2_0
| in_environment(esk1_0,initial_FM_EP(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_31])]) ).
cnf(c_0_39,negated_conjecture,
( ~ greater_or_equal(esk2_0,X1)
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_20]),c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( initial_FM_EP(esk1_0) = esk2_0
| subpopulations(first_movers,efficient_producers,esk1_0,initial_FM_EP(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31])]) ).
cnf(c_0_41,negated_conjecture,
( initial_FM_EP(esk1_0) = esk2_0
| ~ greater_or_equal(esk2_0,initial_FM_EP(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_31])]) ).
cnf(c_0_42,negated_conjecture,
initial_FM_EP(esk1_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_20]),c_0_30]),c_0_31])]) ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_42]),c_0_31])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : MGT020+1 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.13 % 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
% 0.18/0.34 % Computer : n026.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Mon May 4 23:27:08 EDT 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.35 % start to proof: theBenchmark
% 1.26/1.73 % Version : CSE_E---1.7
% 1.26/1.73 % Problem : theBenchmark.p
% 1.26/1.73 % SZS status Theorem for theBenchmark.p
% 1.26/1.73 % SZS output start CNFRefutation
% See solution above
% 1.26/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------