%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% 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 : Tue Sep 8 06:10:20 AM UTC 2026
% Result : Theorem 0.22s 0.47s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 7 12:02:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.22/0.47 GeoParameters:
% 0.22/0.47
% 0.22/0.47 tptp_input = 1
% 0.22/0.47 tptp_output = 0
% 0.22/0.47 nonempty = 1
% 0.22/0.47 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.47 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 0.22/0.47
% 0.22/0.47
% 0.22/0.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.47
% 0.22/0.47 RuleSystem INPUT:
% 0.22/0.47
% 0.22/0.47 Initial Rules:
% 0.22/0.47 #0: input, references = 4, size of lhs = 4:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), environment-{F}(V2), subpopulations-{F}(V0,V1,V2,V3) | in_environment-{T}(V2,V3)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #1: input, references = 4, size of lhs = 6:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2), environment-{F}(V3), P_number_of_organizations-{F}(V3,V4,V5), subpopulations-{F}(V0,V1,V3,V4) | greater-{T}(V5,V2)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #2: input, references = 4, size of lhs = 5:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2), increases-{F}(V3), decreases-{F}(V3) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #3: input, references = 3, size of lhs = 5:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2), greater_or_equal-{F}(V3,V4), V3 == V4 | greater-{T}(V3,V4)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #4: input, references = 4, size of lhs = 10:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2), P_equilibrium-{F}(V3,V4), environment-{F}(V3), P_number_of_organizations-{F}(V3,V5,V6), P_resources-{F}(V3,V5,V7), in_environment-{F}(V3,V5), greater-{F}(V6,V2), greater-{F}(V4,V5) | decreases-{T}(V7)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #5: input, references = 4, size of lhs = 9:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2), P_equilibrium-{F}(V3,V4), environment-{F}(V3), P_number_of_organizations-{F}(V3,V5,V6), P_resources-{F}(V3,V5,V7), in_environment-{F}(V3,V5), greater-{F}(V6,V2) | greater-{T}(V4,V5), constant-{T}(V7)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #6: input, references = 4, size of lhs = 10:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2), environment-{F}(V3), P_resources-{F}(V3,V4,V5), P_disbanding_rate-{F}(V0,V4,V6), P_disbanding_rate-{F}(V1,V4,V7), P_difference-{F}(V6,V7,V8), subpopulations-{F}(V0,V1,V3,V4), decreases-{F}(V5) | increases-{T}(V8)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #7: input, references = 3, size of lhs = 11:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2), environment-{F}(V3), P_resources-{F}(V3,V4,V5), P_disbanding_rate-{F}(V0,V4,V6), P_disbanding_rate-{F}(V1,V4,V7), P_difference-{F}(V6,V7,V8), subpopulations-{F}(V0,V1,V3,V4), constant-{F}(V5), decreases-{F}(V8) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #8: input, references = 5, size of lhs = 3:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2) | EXISTS V3: pppp1-{T}(V3,V0,V1)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #9: input, references = 4, size of lhs = 4:
% 0.22/0.47 pppp1-{F}(V0,V1,V2), P_disbanding_rate-{F}(V1,V0,V3), P_disbanding_rate-{F}(V2,V0,V4), P_difference-{F}(V3,V4,V5) | EXISTS V6: pppp0-{T}(V6,V0,V1,V2)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #10: input, references = 4, size of lhs = 4:
% 0.22/0.47 pppp1-{F}(V0,V1,V2), P_disbanding_rate-{F}(V1,V0,V3), P_disbanding_rate-{F}(V2,V0,V4), P_difference-{F}(V3,V4,V5) | decreases-{T}(V5)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #11: input, references = 4, size of lhs = 1:
% 0.22/0.47 pppp0-{F}(V0,V1,V2,V3) | subpopulations-{T}(V2,V3,V0,V1)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #12: input, references = 4, size of lhs = 1:
% 0.22/0.47 pppp0-{F}(V0,V1,V2,V3) | environment-{T}(V0)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #13: input, references = 4, size of lhs = 0:
% 0.22/0.47 FALSE | EXISTS V0: P_first_movers-{T}(V0)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #14: input, references = 4, size of lhs = 0:
% 0.22/0.47 FALSE | EXISTS V0: P_efficient_producers-{T}(V0)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #15: input, references = 4, size of lhs = 2:
% 0.22/0.47 #-{F} V0, #-{F} V1 | EXISTS V2: P_number_of_organizations-{T}(V0,V1,V2)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #16: input, references = 5, size of lhs = 0:
% 0.22/0.47 FALSE | EXISTS V0: P_zero-{T}(V0)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #17: input, references = 4, size of lhs = 1:
% 0.22/0.47 #-{F} V0 | EXISTS V1: P_equilibrium-{T}(V0,V1)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #18: input, references = 4, size of lhs = 2:
% 0.22/0.47 #-{F} V0, #-{F} V1 | EXISTS V2: P_resources-{T}(V0,V1,V2)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #19: input, references = 4, size of lhs = 2:
% 0.22/0.47 #-{F} V0, #-{F} V1 | EXISTS V2: P_difference-{T}(V0,V1,V2)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #20: input, references = 6, size of lhs = 2:
% 0.22/0.47 #-{F} V0, #-{F} V1 | EXISTS V2: P_disbanding_rate-{T}(V0,V1,V2)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 number of initial rules = 21
% 0.22/0.47
% 0.22/0.47 Simplifiers:
% 0.22/0.47 #21: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 subpopulations-{F}(V0,V1,V2,V3), subpopulations-{F}(V0,V1,V6,V3), V2 == V6 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #22: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 subpopulations-{F}(V0,V1,V2,V3), subpopulations-{F}(V0,V1,V6,V7), V3 == V7 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #23: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 subpopulations-{F}(V0,V1,V2,V3), subpopulations-{F}(V4,V5,V6,V7), V0 == V4 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #24: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 subpopulations-{F}(V0,V1,V2,V3), subpopulations-{F}(V4,V5,V6,V7), V1 == V5 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #25: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 P_first_movers-{F}(V0), P_first_movers-{F}(V1), V0 == V1 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #26: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 P_efficient_producers-{F}(V0), P_efficient_producers-{F}(V1), V0 == V1 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #27: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 P_number_of_organizations-{F}(V0,V1,V2), P_number_of_organizations-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #28: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 P_zero-{F}(V0), P_zero-{F}(V1), V0 == V1 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #29: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 P_equilibrium-{F}(V0,V1), P_equilibrium-{F}(V0,V3), V1 == V3 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #30: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 P_resources-{F}(V0,V1,V2), P_resources-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #31: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 P_difference-{F}(V0,V1,V2), P_difference-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #32: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 P_disbanding_rate-{F}(V0,V1,V2), P_disbanding_rate-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #33: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 pppp0-{F}(V0,V1,V2,V3), pppp0-{F}(V4,V1,V2,V3), V0 == V4 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #34: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 pppp0-{F}(V0,V1,V2,V3), pppp0-{F}(V4,V5,V2,V3), V1 == V5 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #35: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 pppp0-{F}(V0,V1,V2,V3), pppp0-{F}(V4,V5,V6,V7), V2 == V6 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #36: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 pppp0-{F}(V0,V1,V2,V3), pppp0-{F}(V4,V5,V6,V7), V3 == V7 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #37: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 pppp1-{F}(V0,V1,V2), pppp1-{F}(V3,V1,V2), V0 == V3 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #38: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 pppp1-{F}(V0,V1,V2), pppp1-{F}(V3,V4,V5), V1 == V4 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #39: unsound, references = 3, size of lhs = 3:
% 0.22/0.47 pppp1-{F}(V0,V1,V2), pppp1-{F}(V3,V4,V5), V2 == V5 | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 number of simplifiers = 19
% 0.22/0.47
% 0.22/0.47 Learnt:
% 0.22/0.47 #44: mergings( V0 == V8, V1 == V9, V2 == V10; #40 ), references = 2, size of lhs = 16:
% 0.22/0.47 environment-{F}(V0), P_equilibrium-{F}(V0,V1), in_environment-{F}(V0,V2), P_number_of_organizations-{F}(V0,V2,V3), greater-{F}(V3,V4), P_zero-{F}(V4), P_resources-{F}(V0,V2,V5), P_first_movers-{F}(V6), P_efficient_producers-{F}(V7), environment-{F}(V8), subpopulations-{F}(V6,V7,V8,V9), P_resources-{F}(V8,V9,V5), P_disbanding_rate-{F}(V6,V9,V10), P_disbanding_rate-{F}(V7,V9,V11), P_difference-{F}(V10,V11,V12), decreases-{F}(V12) | greater-{T}(V1,V2)
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #70: mergings( V6 == V15, V7 == V16, V11 == V15, V15 == V21, V12 == V16, V16 == V22, V4 == V14, V5 == V13, V13 == V17, V17 == V23, V8 == V18, V9 == V19, V10 == V20; #56 ), references = 1, size of lhs = 13:
% 0.22/0.47 environment-{F}(V0), in_environment-{F}(V0,V1), P_equilibrium-{F}(V0,V2), P_number_of_organizations-{F}(V0,V1,V3), greater-{F}(V3,V4), P_zero-{F}(V4), decreases-{F}(V5), P_first_movers-{F}(V6), P_disbanding_rate-{F}(V6,V1,V7), P_efficient_producers-{F}(V8), subpopulations-{F}(V6,V8,V0,V1), P_disbanding_rate-{F}(V8,V1,V9), P_difference-{F}(V7,V9,V5) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #86: mergings( V3 == V5, V5 == V11, V4 == V6, V6 == V12, V8 == V11, V11 == V20, V9 == V12, V12 == V21, V10 == V13, V13 == V22, V14 == V17, V15 == V18, V7 == V19; #72 ), references = 1, size of lhs = 11:
% 0.22/0.47 environment-{F}(V0), in_environment-{F}(V0,V1), P_equilibrium-{F}(V0,V2), decreases-{F}(V3), P_first_movers-{F}(V4), P_disbanding_rate-{F}(V4,V1,V5), P_efficient_producers-{F}(V6), subpopulations-{F}(V4,V6,V0,V1), P_disbanding_rate-{F}(V6,V1,V7), P_difference-{F}(V5,V7,V3), P_zero-{F}(V8) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #101: mergings( V2 == V4, V4 == V10, V3 == V5, V5 == V11, V7 == V10, V10 == V19, V8 == V11, V11 == V20, V9 == V12, V12 == V21, V14 == V16, V15 == V17, V6 == V18; #87 ), references = 1, size of lhs = 10:
% 0.22/0.47 environment-{F}(V0), in_environment-{F}(V0,V1), decreases-{F}(V2), P_first_movers-{F}(V3), P_disbanding_rate-{F}(V3,V1,V4), P_efficient_producers-{F}(V5), subpopulations-{F}(V3,V5,V0,V1), P_disbanding_rate-{F}(V5,V1,V6), P_difference-{F}(V4,V6,V2), P_zero-{F}(V7) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #118: mergings( V8 == V1, V1 == V13, V9 == V2, V2 == V14, V10 == V11, V11 == V15, V3 == V16, V4 == V17, V5 == V7, V16 == V18, V17 == V19, V7 == V12; #105 ), references = 2, size of lhs = 8:
% 0.22/0.47 decreases-{F}(V0), P_first_movers-{F}(V1), P_efficient_producers-{F}(V2), pppp1-{F}(V3,V1,V2), P_zero-{F}(V4), P_disbanding_rate-{F}(V1,V3,V5), P_disbanding_rate-{F}(V2,V3,V6), P_difference-{F}(V5,V6,V0) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #125: mergings( V3 == V7, V4 == V9, V5 == V8; #121 ), references = 2, size of lhs = 6:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2), pppp1-{F}(V3,V0,V1), P_disbanding_rate-{F}(V0,V3,V4), P_disbanding_rate-{F}(V1,V3,V5) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #127: exists( #20, #121 ), references = 1, size of lhs = 4:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V0), P_zero-{F}(V1), pppp1-{F}(V2,V0,V0) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #130: mergings( V1 == V3; #128 ), references = 1, size of lhs = 3:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V0), P_zero-{F}(V1) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #132: exists( #16, #128 ), references = 1, size of lhs = 2:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V0) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #134: exists( #20, #125 ), references = 1, size of lhs = 5:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2), pppp1-{F}(V3,V0,V1), P_disbanding_rate-{F}(V0,V3,V4) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #136: exists( #20, #133 ), references = 1, size of lhs = 4:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2), pppp1-{F}(V3,V0,V1) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #139: mergings( V2 == V4; #137 ), references = 1, size of lhs = 3:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1), P_zero-{F}(V2) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #141: exists( #16, #137 ), references = 1, size of lhs = 2:
% 0.22/0.47 P_first_movers-{F}(V0), P_efficient_producers-{F}(V1) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #143: exists( #14, #140 ), references = 1, size of lhs = 1:
% 0.22/0.47 P_first_movers-{F}(V0) | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 #145: exists( #13, #142 ), references = 1, size of lhs = 0:
% 0.22/0.47 FALSE | FALSE
% 0.22/0.47 (used 0 times, uses = {})
% 0.22/0.47
% 0.22/0.47 number of learnt formulas = 15
% 0.22/0.47
% 0.22/0.47
% 0.22/0.47 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.47
% 0.22/0.47 randbase = 1
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