%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : MGT036+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 : Thu Sep 24 01:27:57 PM UTC 2026
% Result : Theorem 0.15s 0.58s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 151 ( 64 ~; 52 |; 22 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 96 ( 13 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t5,conjecture,
! [X1,X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& environment(X1) )
=> ~ outcompetes(first_movers,efficient_producers,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5) ).
fof(a13,hypothesis,
! [X1,X2,X3,X4] :
( ( greater(resilience(X3),resilience(X2))
& ~ greater(zero,growth_rate(X2,X4))
& in_environment(X1,X4)
& environment(X1) )
=> ~ greater(zero,growth_rate(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13) ).
fof(mp_growth_rate_relationships,axiom,
! [X1,X2,X3,X4] :
( ( ( subpopulations(X2,X3,X1,X4)
& environment(X1) )
=> greater_or_equal(growth_rate(X2,X4),zero) )
<=> ~ greater(zero,growth_rate(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
fof(mp_symmetry_of_subpopulations,axiom,
! [X1,X2,X3,X4] :
( ( subpopulations(X2,X3,X1,X4)
& environment(X1) )
=> subpopulations(X3,X2,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(d2,hypothesis,
! [X1,X2,X3,X4] :
( ( subpopulations(X2,X3,X1,X4)
& environment(X1) )
=> ( ( greater(zero,growth_rate(X2,X4))
& greater_or_equal(growth_rate(X3,X4),zero) )
<=> outcompetes(X3,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(mp_time_point_occur,axiom,
! [X1,X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& environment(X1) )
=> in_environment(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& environment(X1) )
=> ~ outcompetes(first_movers,efficient_producers,X4) ),
inference(assume_negation,[status(cth)],[prove_t5]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& environment(X1) )
=> ~ outcompetes(first_movers,efficient_producers,X4) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_9,hypothesis,
! [X1,X2,X3,X4] :
( ( greater(resilience(X3),resilience(X2))
& ~ greater(zero,growth_rate(X2,X4))
& in_environment(X1,X4)
& environment(X1) )
=> ~ greater(zero,growth_rate(X3,X4)) ),
inference(fof_simplification,[status(thm)],[a13]) ).
fof(c_0_10,plain,
! [X1,X2,X3,X4] :
( ( ( subpopulations(X2,X3,X1,X4)
& environment(X1) )
=> greater_or_equal(growth_rate(X2,X4),zero) )
<=> ~ greater(zero,growth_rate(X2,X4)) ),
inference(fof_simplification,[status(thm)],[mp_growth_rate_relationships]) ).
fof(c_0_11,plain,
! [X5,X6,X7,X8] :
( subpopulations(X7,X6,X5,X8)
| ~ subpopulations(X6,X7,X5,X8)
| ~ environment(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations])])]) ).
fof(c_0_12,negated_conjecture,
( outcompetes(first_movers,efficient_producers,esk2_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& environment(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_13,hypothesis,
! [X19,X20,X21,X22] :
( ~ greater(zero,growth_rate(X21,X22))
| ~ greater(resilience(X21),resilience(X20))
| greater(zero,growth_rate(X20,X22))
| ~ in_environment(X19,X22)
| ~ environment(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_14,plain,
! [X11,X12,X13,X14] :
( ( greater_or_equal(growth_rate(X12,X14),zero)
| ~ subpopulations(X12,X13,X11,X14)
| ~ environment(X11)
| greater(zero,growth_rate(X12,X14)) )
& ( ~ greater(zero,growth_rate(X12,X14))
| ~ greater_or_equal(growth_rate(X12,X14),zero) )
& ( ~ greater(zero,growth_rate(X12,X14))
| subpopulations(X12,X13,X11,X14) )
& ( ~ greater(zero,growth_rate(X12,X14))
| environment(X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_15,hypothesis,
! [X15,X16,X17,X18] :
( ( ~ subpopulations(X16,X17,X15,X18)
| ~ environment(X15)
| ~ outcompetes(X17,X16,X18)
| greater(zero,growth_rate(X16,X18)) )
& ( ~ subpopulations(X16,X17,X15,X18)
| ~ environment(X15)
| ~ outcompetes(X17,X16,X18)
| greater_or_equal(growth_rate(X17,X18),zero) )
& ( ~ subpopulations(X16,X17,X15,X18)
| ~ environment(X15)
| outcompetes(X17,X16,X18)
| ~ greater(zero,growth_rate(X16,X18))
| ~ greater_or_equal(growth_rate(X17,X18),zero) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2])])])]) ).
cnf(c_0_16,plain,
( ~ subpopulations(X2,X3,X1,X4)
| ~ environment(X1)
| subpopulations(X3,X2,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
( ~ greater(zero,growth_rate(X4,X2))
| ~ greater(resilience(X4),resilience(X3))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(zero,growth_rate(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ greater(zero,growth_rate(X2,X3))
| environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,hypothesis,
( ~ subpopulations(X1,X3,X4,X2)
| ~ environment(X4)
| ~ outcompetes(X3,X1,X2)
| greater(zero,growth_rate(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
subpopulations(efficient_producers,first_movers,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_23,negated_conjecture,
outcompetes(first_movers,efficient_producers,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,hypothesis,
( ~ in_environment(X4,X2)
| ~ greater(resilience(X3),resilience(X1))
| ~ greater(zero,growth_rate(X3,X2))
| greater(zero,growth_rate(X1,X2)) ),
inference(csr,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
greater(zero,growth_rate(efficient_producers,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_18])]) ).
fof(c_0_26,plain,
! [X9,X10] :
( in_environment(X9,X10)
| ~ subpopulations(first_movers,efficient_producers,X9,X10)
| ~ environment(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_point_occur])])]) ).
cnf(c_0_27,hypothesis,
( ~ in_environment(X2,esk2_0)
| ~ greater(resilience(efficient_producers),resilience(X1))
| greater(zero,growth_rate(X1,esk2_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[a2]) ).
cnf(c_0_29,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
environment(X1),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_31,hypothesis,
( ~ subpopulations(X3,X1,X4,X2)
| ~ environment(X4)
| ~ outcompetes(X1,X3,X2)
| greater_or_equal(growth_rate(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,hypothesis,
( ~ in_environment(X1,esk2_0)
| greater(zero,growth_rate(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| in_environment(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_34,plain,
( ~ greater(zero,growth_rate(X1,X4))
| subpopulations(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_35,hypothesis,
( ~ subpopulations(X3,X1,X4,X2)
| ~ outcompetes(X1,X3,X2)
| greater_or_equal(growth_rate(X1,X2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_30])]) ).
cnf(c_0_36,hypothesis,
( ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
| greater(zero,growth_rate(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
( ~ greater(zero,growth_rate(X2,X4))
| subpopulations(X1,X2,X3,X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_34]),c_0_20]) ).
cnf(c_0_38,plain,
( ~ greater(zero,growth_rate(X1,X2))
| ~ greater_or_equal(growth_rate(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_39,negated_conjecture,
greater_or_equal(growth_rate(first_movers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_22]),c_0_23])]) ).
cnf(c_0_40,hypothesis,
greater(zero,growth_rate(first_movers,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_25])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.51 % Computer : n005.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Mon Sep 21 01:22:18 UTC 2026
% 0.09/0.51 % CPUTime :
% 0.09/0.51 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.56 Running first-order theorem proving
% 0.15/0.56 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.58 % Version: 3.5.1
% 0.15/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.58 % Starting sh5l with 300s (1) cores
% 0.15/0.58 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2237719 completed with status 0
% 0.15/0.58 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.58 % No SInE strategy applied
% 0.15/0.58 % Search class: FGHNF-FFSS21-SFFFFFNN
% 0.15/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.58 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/0.58 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.58 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.58 % SubtermCWHack with pid 2237723 completed with status 0
% 0.15/0.58 % Result found by SubtermCWHack
% 0.15/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.58 % No SInE strategy applied
% 0.15/0.58 % Search class: FGHNF-FFSS21-SFFFFFNN
% 0.15/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.58 % Preprocessing time : 0.001 s
% 0.15/0.58
% 0.15/0.58 % Proof found!
% 0.15/0.58 % SZS status Theorem
% 0.15/0.58 % SZS output start CNFRefutation
% See solution above
% 0.15/0.58 % Parsed axioms : 7
% 0.15/0.58 % Removed by relevancy pruning/SinE : 0
% 0.15/0.58 % Initial clauses : 14
% 0.15/0.58 % Removed in clause preprocessing : 0
% 0.15/0.58 % Initial clauses in saturation : 14
% 0.15/0.58 % Processed clauses : 34
% 0.15/0.58 % ...of these trivial : 0
% 0.15/0.58 % ...subsumed : 4
% 0.15/0.58 % ...remaining for further processing : 30
% 0.15/0.58 % Other redundant clauses eliminated : 0
% 0.15/0.58 % Clauses deleted for lack of memory : 0
% 0.15/0.58 % Backward-subsumed : 0
% 0.15/0.58 % Backward-rewritten : 8
% 0.15/0.58 % Generated clauses : 38
% 0.15/0.58 % ...of the previous two non-redundant : 27
% 0.15/0.58 % ...aggressively subsumed : 0
% 0.15/0.58 % Contextual simplify-reflections : 2
% 0.15/0.58 % Paramodulations : 38
% 0.15/0.58 % Factorizations : 0
% 0.15/0.58 % NegExts : 0
% 0.15/0.58 % Equation resolutions : 0
% 0.15/0.58 % Disequality decompositions : 0
% 0.15/0.58 % Total rewrite steps : 27
% 0.15/0.58 % ...of those cached : 17
% 0.15/0.58 % Propositional unsat checks : 0
% 0.15/0.58 % Propositional check models : 0
% 0.15/0.58 % Propositional check unsatisfiable : 0
% 0.15/0.58 % Propositional clauses : 0
% 0.15/0.58 % Propositional clauses after purity: 0
% 0.15/0.58 % Propositional unsat core size : 0
% 0.15/0.58 % Propositional preprocessing time : 0.000
% 0.15/0.58 % Propositional encoding time : 0.000
% 0.15/0.58 % Propositional solver time : 0.000
% 0.15/0.58 % Success case prop preproc time : 0.000
% 0.15/0.58 % Success case prop encoding time : 0.000
% 0.15/0.58 % Success case prop solver time : 0.000
% 0.15/0.58 % Current number of processed clauses : 22
% 0.15/0.58 % Positive orientable unit clauses : 8
% 0.15/0.58 % Positive unorientable unit clauses: 0
% 0.15/0.58 % Negative unit clauses : 0
% 0.15/0.58 % Non-unit-clauses : 14
% 0.15/0.58 % Current number of unprocessed clauses: 5
% 0.15/0.58 % ...number of literals in the above : 17
% 0.15/0.58 % Current number of archived formulas : 0
% 0.15/0.58 % Current number of archived clauses : 8
% 0.15/0.58 % Clause-clause subsumption calls (NU) : 40
% 0.15/0.58 % Rec. Clause-clause subsumption calls : 35
% 0.15/0.58 % Non-unit clause-clause subsumptions : 6
% 0.15/0.58 % Unit Clause-clause subsumption calls : 3
% 0.15/0.58 % Rewrite failures with RHS unbound : 0
% 0.15/0.58 % BW rewrite match attempts : 5
% 0.15/0.58 % BW rewrite match successes : 5
% 0.15/0.58 % Condensation attempts : 0
% 0.15/0.58 % Condensation successes : 0
% 0.15/0.58 % Termbank termtop insertions : 1775
% 0.15/0.58 % Search garbage collected termcells : 223
% 0.15/0.58
% 0.15/0.58 % -------------------------------------------------
% 0.15/0.58 % User time : 0.006 s
% 0.15/0.58 % System time : 0.002 s
% 0.15/0.58 % Total time : 0.008 s
% 0.15/0.58 % Maximum resident set size: 3636 pages
% 0.15/0.58
% 0.15/0.58 % -------------------------------------------------
% 0.15/0.58 % User time : 0.016 s
% 0.15/0.58 % System time : 0.009 s
% 0.15/0.58 % Total time : 0.025 s
% 0.15/0.58 % Maximum resident set size: 4608 pages
% 0.15/0.58 % E exiting
%------------------------------------------------------------------------------