%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : MGT023+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n006.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 06:10:21 AM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 7 12:05:46 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.44 GeoParameters:
% 0.13/0.44
% 0.13/0.44 tptp_input = 1
% 0.13/0.44 tptp_output = 0
% 0.13/0.44 nonempty = 1
% 0.13/0.44 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.44 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 0.13/0.44
% 0.13/0.44
% 0.13/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.44
% 0.13/0.44 RuleSystem INPUT:
% 0.13/0.44
% 0.13/0.44 Initial Rules:
% 0.13/0.44 #0: input, references = 5, size of lhs = 8:
% 0.13/0.44 P_efficient_producers-{F}(V0), P_first_movers-{F}(V1), P_growth_rate-{F}(V0,V2,V3), P_growth_rate-{F}(V1,V2,V4), P_critical_point-{F}(V5,V6), environment-{F}(V5), in_environment-{F}(V5,V2), V2 == V6 | greater-{T}(V3,V4), pppp3-{T}(V5,V2,V0,V1)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #1: input, references = 5, size of lhs = 1:
% 0.13/0.44 pppp3-{F}(V0,V1,V2,V3) | EXISTS V4: pppp0-{T}(V0,V1,V4,V2,V3)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #2: input, references = 5, size of lhs = 4:
% 0.13/0.44 pppp0-{F}(V0,V1,V2,V3,V4), P_growth_rate-{F}(V3,V2,V5), P_growth_rate-{F}(V4,V2,V6), greater-{F}(V5,V6) | FALSE
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #3: input, references = 5, size of lhs = 3:
% 0.13/0.44 pppp0-{F}(V0,V1,V2,V3,V4), P_growth_rate-{F}(V3,V2,V5), P_growth_rate-{F}(V4,V2,V6) | greater-{T}(V2,V1)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #4: input, references = 5, size of lhs = 3:
% 0.13/0.44 pppp0-{F}(V0,V1,V2,V3,V4), P_growth_rate-{F}(V3,V2,V5), P_growth_rate-{F}(V4,V2,V6) | subpopulations-{T}(V4,V3,V0,V2)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #5: input, references = 5, size of lhs = 4:
% 0.13/0.44 P_efficient_producers-{F}(V0), P_first_movers-{F}(V1), environment-{F}(V2), stable-{F}(V2) | EXISTS V3: pppp1-{T}(V2,V3,V0,V1)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #6: input, references = 5, size of lhs = 7:
% 0.13/0.44 pppp1-{F}(V0,V1,V2,V3), P_growth_rate-{F}(V2,V1,V4), P_growth_rate-{F}(V3,V1,V5), P_growth_rate-{F}(V2,V6,V7), P_growth_rate-{F}(V3,V6,V8), subpopulations-{F}(V3,V2,V0,V6), greater-{F}(V6,V1) | greater-{T}(V7,V8)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #7: input, references = 4, size of lhs = 4:
% 0.13/0.44 pppp1-{F}(V0,V1,V2,V3), P_growth_rate-{F}(V2,V1,V4), P_growth_rate-{F}(V3,V1,V5), greater-{F}(V4,V5) | FALSE
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #8: input, references = 7, size of lhs = 3:
% 0.13/0.44 pppp1-{F}(V0,V1,V2,V3), P_growth_rate-{F}(V2,V1,V4), P_growth_rate-{F}(V3,V1,V5) | in_environment-{T}(V0,V1)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #9: input, references = 5, size of lhs = 2:
% 0.13/0.44 P_efficient_producers-{F}(V0), P_first_movers-{F}(V1) | EXISTS V2: pppp2-{T}(V2)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #10: input, references = 5, size of lhs = 3:
% 0.13/0.44 pppp2-{F}(V0), P_critical_point-{F}(V0,V1), in_environment-{F}(V0,V1) | FALSE
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #11: input, references = 5, size of lhs = 2:
% 0.13/0.44 pppp2-{F}(V0), P_critical_point-{F}(V0,V1) | stable-{T}(V0)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #12: input, references = 5, size of lhs = 2:
% 0.13/0.44 pppp2-{F}(V0), P_critical_point-{F}(V0,V1) | environment-{T}(V0)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #13: input, references = 12, size of lhs = 2:
% 0.13/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_growth_rate-{T}(V0,V1,V2)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #14: input, references = 4, size of lhs = 0:
% 0.13/0.44 FALSE | EXISTS V0: P_efficient_producers-{T}(V0)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #15: input, references = 4, size of lhs = 0:
% 0.13/0.44 FALSE | EXISTS V0: P_first_movers-{T}(V0)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #16: input, references = 5, size of lhs = 1:
% 0.13/0.44 #-{F} V0 | EXISTS V1: P_critical_point-{T}(V0,V1)
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 number of initial rules = 17
% 0.13/0.44
% 0.13/0.44 Simplifiers:
% 0.13/0.44 #17: unsound, references = 3, size of lhs = 3:
% 0.13/0.44 environment-{F}(V0), environment-{F}(V1), V0 == V1 | FALSE
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #18: unsound, references = 3, size of lhs = 3:
% 0.13/0.44 in_environment-{F}(V0,V1), in_environment-{F}(V2,V3), V0 == V2 | FALSE
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #19: unsound, references = 3, size of lhs = 3:
% 0.13/0.44 subpopulations-{F}(V0,V1,V2,V3), subpopulations-{F}(V4,V5,V6,V7), V1 == V5 | FALSE
% 0.13/0.44 (used 0 times, uses = {})
% 0.13/0.44
% 0.13/0.44 #20: unsound, references = 3, size of lhs = 3:
% 0.13/0.44 subpopulations-{F}(V0,V1,V2,V3), subpopulations-{F}(V4,V5,V6,V7), V0 == V4 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #21: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 subpopulations-{F}(V0,V1,V2,V3), subpopulations-{F}(V4,V5,V6,V7), V2 == V6 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #22: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 stable-{F}(V0), stable-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #23: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_growth_rate-{F}(V0,V1,V2), P_growth_rate-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #24: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_efficient_producers-{F}(V0), P_efficient_producers-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #25: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_first_movers-{F}(V0), P_first_movers-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #26: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_critical_point-{F}(V0,V1), P_critical_point-{F}(V0,V3), V1 == V3 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #27: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp0-{F}(V0,V1,V2,V3,V4), pppp0-{F}(V0,V1,V7,V3,V4), V2 == V7 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #28: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp0-{F}(V0,V1,V2,V3,V4), pppp0-{F}(V5,V6,V7,V8,V9), V3 == V8 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #29: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp0-{F}(V0,V1,V2,V3,V4), pppp0-{F}(V5,V6,V7,V8,V9), V4 == V9 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #30: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp0-{F}(V0,V1,V2,V3,V4), pppp0-{F}(V5,V6,V7,V8,V9), V0 == V5 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #31: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp1-{F}(V0,V1,V2,V3), pppp1-{F}(V0,V5,V2,V3), V1 == V5 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #32: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp1-{F}(V0,V1,V2,V3), pppp1-{F}(V4,V5,V6,V7), V2 == V6 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #33: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp1-{F}(V0,V1,V2,V3), pppp1-{F}(V4,V5,V6,V7), V3 == V7 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #34: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp1-{F}(V0,V1,V2,V3), pppp1-{F}(V4,V5,V6,V7), V0 == V4 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #35: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp2-{F}(V0), pppp2-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #36: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp3-{F}(V0,V1,V2,V3), pppp3-{F}(V4,V5,V6,V7), V2 == V6 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #37: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp3-{F}(V0,V1,V2,V3), pppp3-{F}(V4,V5,V6,V7), V3 == V7 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #38: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 pppp3-{F}(V0,V1,V2,V3), pppp3-{F}(V4,V5,V6,V7), V0 == V4 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 number of simplifiers = 22
% 0.13/0.45
% 0.13/0.45 Learnt:
% 0.13/0.45 #52: mergings( V4 == V8, V5 == V6, V6 == V9; #48 ), references = 1, size of lhs = 5:
% 0.13/0.45 pppp1-{F}(V0,V1,V2,V2), P_growth_rate-{F}(V2,V1,V3), pppp0-{F}(V0,V1,V4,V2,V2), pppp0-{F}(V0,V5,V4,V2,V2), pppp0-{F}(V0,V6,V4,V2,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #55: mergings( V4 == V5; #53 ), references = 1, size of lhs = 3:
% 0.13/0.45 pppp3-{F}(V0,V1,V2,V2), pppp1-{F}(V0,V1,V2,V2), P_growth_rate-{F}(V2,V1,V3) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #60: mergings( V2 == V3, V3 == V6, V6 == V7; #56 ), references = 1, size of lhs = 8:
% 0.13/0.45 P_efficient_producers-{F}(V0), P_first_movers-{F}(V0), environment-{F}(V1), P_critical_point-{F}(V1,V2), in_environment-{F}(V1,V3), V3 == V2, pppp1-{F}(V1,V3,V0,V0), P_growth_rate-{F}(V0,V3,V4) | greater-{T}(V4,V4)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #65: mergings( V3 == V5; #63 ), references = 1, size of lhs = 6:
% 0.13/0.45 P_efficient_producers-{F}(V0), P_first_movers-{F}(V0), environment-{F}(V1), P_critical_point-{F}(V1,V2), pppp1-{F}(V1,V3,V0,V0), V3 == V2 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #67: exists( #5, #63 ), references = 2, size of lhs = 5:
% 0.13/0.45 stable-{F}(V0), environment-{F}(V0), P_efficient_producers-{F}(V1), P_first_movers-{F}(V1), P_critical_point-{F}(V0,V2) | pppp1-{T}(V0,V2,V1,V1)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #70: exists( #13, #68 ), references = 2, size of lhs = 3:
% 0.13/0.45 pppp2-{F}(V0), P_critical_point-{F}(V0,V1), pppp1-{F}(V0,V1,V2,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #78: exists( #16, #76 ), references = 1, size of lhs = 3:
% 0.13/0.45 pppp2-{F}(V0), P_efficient_producers-{F}(V1), P_first_movers-{F}(V1) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #82: mergings( V0 == V3, V1 == V3; #79 ), references = 1, size of lhs = 2:
% 0.13/0.45 P_efficient_producers-{F}(V0), P_first_movers-{F}(V0) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #84: disj( #0, input ), references = 1, size of lhs = 11:
% 0.13/0.45 P_efficient_producers-{F}(V0), P_first_movers-{F}(V1), environment-{F}(V2), P_critical_point-{F}(V2,V3), in_environment-{F}(V2,V4), V4 == V3, P_growth_rate-{F}(V0,V4,V5), P_growth_rate-{F}(V1,V4,V6), P_growth_rate-{F}(V7,V8,V5), P_growth_rate-{F}(V9,V8,V6), pppp1-{F}(V10,V8,V7,V9) | pppp3-{T}(V2,V4,V0,V1)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #101: mergings( V6 == V7, V3 == V5, V4 == V7, V5 == V14, V10 == V11, V11 == V15; #94 ), references = 1, size of lhs = 7:
% 0.13/0.45 P_growth_rate-{F}(V0,V1,V2), P_growth_rate-{F}(V0,V3,V4), pppp0-{F}(V5,V3,V1,V0,V6), pppp1-{F}(V5,V3,V0,V6), pppp0-{F}(V5,V7,V1,V0,V6), P_growth_rate-{F}(V6,V3,V8), pppp0-{F}(V5,V9,V1,V0,V6) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #105: mergings( V5 == V7, V7 == V10; #102 ), references = 1, size of lhs = 6:
% 0.13/0.45 P_growth_rate-{F}(V0,V1,V2), pppp1-{F}(V3,V1,V0,V4), P_growth_rate-{F}(V4,V1,V5), pppp0-{F}(V3,V1,V6,V0,V4), pppp0-{F}(V3,V7,V6,V0,V4), pppp0-{F}(V3,V8,V6,V0,V4) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #107: exists( #1, #102 ), references = 1, size of lhs = 4:
% 0.13/0.45 P_growth_rate-{F}(V0,V1,V2), pppp3-{F}(V3,V1,V0,V4), pppp1-{F}(V3,V1,V0,V4), P_growth_rate-{F}(V4,V1,V5) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #116: mergings( V6 == V7, V3 == V8, V7 == V9, V8 == V10, V4 == V11; #110 ), references = 1, size of lhs = 7:
% 0.13/0.45 P_efficient_producers-{F}(V0), P_first_movers-{F}(V1), environment-{F}(V2), P_critical_point-{F}(V2,V3), pppp1-{F}(V2,V4,V0,V1), V4 == V3, P_growth_rate-{F}(V1,V4,V5) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #119: mergings( V4 == V6; #117 ), references = 1, size of lhs = 6:
% 0.13/0.45 P_efficient_producers-{F}(V0), P_first_movers-{F}(V1), environment-{F}(V2), P_critical_point-{F}(V2,V3), pppp1-{F}(V2,V4,V0,V1), V4 == V3 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #121: exists( #5, #117 ), references = 2, size of lhs = 5:
% 0.13/0.45 stable-{F}(V0), environment-{F}(V0), P_efficient_producers-{F}(V1), P_first_movers-{F}(V2), P_critical_point-{F}(V0,V3) | pppp1-{T}(V0,V3,V1,V2)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #124: exists( #13, #122 ), references = 1, size of lhs = 4:
% 0.13/0.45 pppp2-{F}(V0), P_critical_point-{F}(V0,V1), pppp1-{F}(V0,V1,V2,V3), P_growth_rate-{F}(V2,V1,V4) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #126: exists( #13, #123 ), references = 2, size of lhs = 3:
% 0.13/0.45 pppp2-{F}(V0), P_critical_point-{F}(V0,V1), pppp1-{F}(V0,V1,V2,V3) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #137: exists( #16, #134 ), references = 1, size of lhs = 3:
% 0.13/0.45 pppp2-{F}(V0), P_efficient_producers-{F}(V1), P_first_movers-{F}(V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #141: mergings( V0 == V3, V1 == V4; #138 ), references = 1, size of lhs = 2:
% 0.13/0.45 P_efficient_producers-{F}(V0), P_first_movers-{F}(V1) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #144: mergings( V1 == V2; #142 ), references = 1, size of lhs = 1:
% 0.13/0.45 P_efficient_producers-{F}(V0) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #146: exists( #14, #142 ), references = 1, size of lhs = 0:
% 0.13/0.45 FALSE | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 number of learnt formulas = 21
% 0.13/0.45
% 0.13/0.45
% 0.13/0.45 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.45
% 0.13/0.45 randbase = 1
%------------------------------------------------------------------------------