TSTP Solution File: HAL002+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : HAL002+1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n019.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 : Sat Jul 23 06:04:38 EDT 2022
% Result : Theorem 1.68s 1.85s
% Output : Refutation 1.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : HAL002+1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jul 22 10:35:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.85 GeoParameters:
% 1.68/1.85
% 1.68/1.85 tptp_input = 1
% 1.68/1.85 tptp_output = 0
% 1.68/1.85 nonempty = 1
% 1.68/1.85 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.68/1.85 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 1.68/1.85
% 1.68/1.85
% 1.68/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.68/1.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.68/1.85
% 1.68/1.85 RuleSystem INPUT:
% 1.68/1.85
% 1.68/1.85 Initial Rules:
% 1.68/1.85 #0: input, references = 4, size of lhs = 6:
% 1.68/1.85 P_zero-{F}(V1,V3), P_apply-{F}(V0,V3,V4), P_zero-{F}(V2,V5), morphism-{F}(V0,V1,V2), P_apply-{F}(V0,V6,V7), element-{F}(V6,V1) | element-{T}(V7,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #1: input, references = 4, size of lhs = 5:
% 1.68/1.85 P_zero-{F}(V1,V3), P_apply-{F}(V0,V3,V4), P_zero-{F}(V2,V5), morphism-{F}(V0,V1,V2), V4 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #2: input, references = 4, size of lhs = 7:
% 1.68/1.85 injection-{F}(V0), P_apply-{F}(V0,V2,V3), element-{F}(V2,V1), P_apply-{F}(V0,V4,V3), element-{F}(V4,V1), morphism-{F}(V0,V1,V6), V4 == V2 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #3: input, references = 4, size of lhs = 1:
% 1.68/1.85 morphism-{F}(V0,V1,V2) | injection-{T}(V0), pppp13-{T}(V0,V1)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #4: input, references = 5, size of lhs = 1:
% 1.68/1.85 pppp13-{F}(V0,V1) | EXISTS V2: pppp5-{T}(V0,V1,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #5: input, references = 4, size of lhs = 2:
% 1.68/1.85 pppp5-{F}(V0,V1,V2), P_apply-{F}(V0,V2,V3) | EXISTS V4: pppp4-{T}(V0,V1,V4,V2,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #6: input, references = 5, size of lhs = 2:
% 1.68/1.85 pppp5-{F}(V0,V1,V2), P_apply-{F}(V0,V2,V3) | element-{T}(V2,V1)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #7: input, references = 4, size of lhs = 2:
% 1.68/1.85 pppp4-{F}(V0,V1,V3,V3,V4), P_apply-{F}(V0,V3,V5) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #8: input, references = 4, size of lhs = 3:
% 1.68/1.85 pppp4-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V0,V2,V5), V5 == V4 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #9: input, references = 4, size of lhs = 2:
% 1.68/1.85 pppp4-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V0,V2,V5) | element-{T}(V2,V1)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #10: input, references = 4, size of lhs = 3:
% 1.68/1.85 surjection-{F}(V0), morphism-{F}(V0,V2,V1), element-{F}(V3,V1) | EXISTS V4: pppp6-{T}(V0,V2,V3,V4)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #11: input, references = 4, size of lhs = 3:
% 1.68/1.85 pppp6-{F}(V0,V1,V2,V3), P_apply-{F}(V0,V3,V4), V4 == V2 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #12: input, references = 4, size of lhs = 2:
% 1.68/1.85 pppp6-{F}(V0,V1,V2,V3), P_apply-{F}(V0,V3,V4) | element-{T}(V3,V1)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #13: input, references = 3, size of lhs = 1:
% 1.68/1.85 morphism-{F}(V0,V2,V1) | surjection-{T}(V0), pppp14-{T}(V0,V2,V1)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #14: input, references = 3, size of lhs = 1:
% 1.68/1.85 pppp14-{F}(V0,V1,V2) | EXISTS V3: pppp7-{T}(V0,V1,V2,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #15: input, references = 3, size of lhs = 3:
% 1.68/1.85 pppp7-{F}(V0,V1,V2,V3), P_apply-{F}(V0,V4,V3), element-{F}(V4,V1) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #16: input, references = 3, size of lhs = 1:
% 1.68/1.85 pppp7-{F}(V0,V1,V2,V3) | element-{T}(V3,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #17: input, references = 3, size of lhs = 4:
% 1.68/1.85 morphism-{F}(V0,V1,V2), exact-{F}(V3,V0), morphism-{F}(V3,V4,V1), pppp0-{F}(V2,V0,V1,V5) | pppp1-{T}(V4,V3,V5)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #18: input, references = 3, size of lhs = 4:
% 1.68/1.85 morphism-{F}(V0,V1,V2), exact-{F}(V3,V0), morphism-{F}(V3,V4,V1), pppp1-{F}(V4,V3,V5) | pppp0-{T}(V2,V0,V1,V5)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #19: input, references = 5, size of lhs = 1:
% 1.68/1.85 pppp1-{F}(V0,V1,V2) | EXISTS V3: pppp8-{T}(V0,V3,V1,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #20: input, references = 3, size of lhs = 2:
% 1.68/1.85 P_apply-{F}(V1,V3,V2), element-{F}(V3,V0) | pppp1-{T}(V0,V1,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #21: input, references = 4, size of lhs = 3:
% 1.68/1.85 pppp8-{F}(V0,V1,V2,V3), P_apply-{F}(V2,V1,V4), V4 == V3 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #22: input, references = 5, size of lhs = 2:
% 1.68/1.85 pppp8-{F}(V0,V1,V2,V3), P_apply-{F}(V2,V1,V4) | element-{T}(V1,V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #23: input, references = 3, size of lhs = 3:
% 1.68/1.85 P_apply-{F}(V1,V3,V4), P_zero-{F}(V0,V5), pppp0-{F}(V0,V1,V2,V3) | element-{T}(V3,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #24: input, references = 3, size of lhs = 4:
% 1.68/1.85 P_apply-{F}(V1,V3,V4), P_zero-{F}(V0,V5), pppp0-{F}(V0,V1,V2,V3), V4 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #25: input, references = 3, size of lhs = 3:
% 1.68/1.85 P_apply-{F}(V1,V3,V5), P_zero-{F}(V0,V5), element-{F}(V3,V2) | pppp0-{T}(V0,V1,V2,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #26: input, references = 3, size of lhs = 2:
% 1.68/1.85 morphism-{F}(V0,V1,V2), morphism-{F}(V3,V4,V1) | exact-{T}(V3,V0), pppp15-{T}(V4,V2,V3,V0,V1)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #27: input, references = 3, size of lhs = 1:
% 1.68/1.85 pppp15-{F}(V0,V1,V2,V3,V4) | EXISTS V5: pppp9-{T}(V0,V1,V2,V3,V4,V5)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #28: input, references = 3, size of lhs = 3:
% 1.68/1.85 pppp9-{F}(V0,V1,V2,V3,V4,V5), pppp3-{F}(V0,V2,V5), pppp2-{F}(V1,V3,V4,V5) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #29: input, references = 5, size of lhs = 1:
% 1.68/1.85 pppp9-{F}(V0,V1,V2,V3,V4,V5) | pppp2-{T}(V1,V3,V4,V5), pppp3-{T}(V0,V2,V5)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #30: input, references = 5, size of lhs = 1:
% 1.68/1.85 pppp3-{F}(V0,V1,V2) | EXISTS V3: pppp10-{T}(V0,V3,V1,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #31: input, references = 3, size of lhs = 2:
% 1.68/1.85 P_apply-{F}(V1,V3,V2), element-{F}(V3,V0) | pppp3-{T}(V0,V1,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #32: input, references = 4, size of lhs = 3:
% 1.68/1.85 pppp10-{F}(V0,V1,V2,V3), P_apply-{F}(V2,V1,V4), V4 == V3 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #33: input, references = 5, size of lhs = 2:
% 1.68/1.85 pppp10-{F}(V0,V1,V2,V3), P_apply-{F}(V2,V1,V4) | element-{T}(V1,V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #34: input, references = 3, size of lhs = 3:
% 1.68/1.85 P_apply-{F}(V1,V3,V4), P_zero-{F}(V0,V5), pppp2-{F}(V0,V1,V2,V3) | element-{T}(V3,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #35: input, references = 5, size of lhs = 4:
% 1.68/1.85 P_apply-{F}(V1,V3,V4), P_zero-{F}(V0,V5), pppp2-{F}(V0,V1,V2,V3), V4 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #36: input, references = 3, size of lhs = 3:
% 1.68/1.85 P_apply-{F}(V1,V3,V5), P_zero-{F}(V0,V5), element-{F}(V3,V2) | pppp2-{T}(V0,V1,V2,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #37: input, references = 3, size of lhs = 11:
% 1.68/1.85 commute-{F}(V0,V1,V2,V3), P_apply-{F}(V0,V5,V6), P_apply-{F}(V1,V6,V7), P_apply-{F}(V2,V5,V8), P_apply-{F}(V3,V8,V9), element-{F}(V5,V4), morphism-{F}(V0,V4,V11), morphism-{F}(V1,V11,V10), morphism-{F}(V2,V4,V12), morphism-{F}(V3,V12,V10), V7 == V9 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #38: input, references = 3, size of lhs = 4:
% 1.68/1.85 morphism-{F}(V0,V4,V6), morphism-{F}(V1,V6,V5), morphism-{F}(V2,V4,V7), morphism-{F}(V3,V7,V5) | commute-{T}(V0,V1,V2,V3), pppp16-{T}(V4,V0,V1,V2,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #39: input, references = 3, size of lhs = 1:
% 1.68/1.85 pppp16-{F}(V0,V1,V2,V3,V4) | EXISTS V5: pppp11-{T}(V0,V5,V1,V2,V3,V4)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #40: input, references = 3, size of lhs = 5:
% 1.68/1.85 pppp11-{F}(V0,V1,V2,V3,V4,V5), P_apply-{F}(V2,V1,V6), P_apply-{F}(V3,V6,V9), P_apply-{F}(V4,V1,V8), P_apply-{F}(V5,V8,V9) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #41: input, references = 3, size of lhs = 5:
% 1.68/1.85 pppp11-{F}(V0,V1,V2,V3,V4,V5), P_apply-{F}(V2,V1,V6), P_apply-{F}(V3,V6,V7), P_apply-{F}(V4,V1,V8), P_apply-{F}(V5,V8,V9) | element-{T}(V1,V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #42: input, references = 6, size of lhs = 3:
% 1.68/1.85 element-{F}(V1,V0), P_subtract-{F}(V0,V2,V1,V3), element-{F}(V2,V0) | element-{T}(V3,V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #43: input, references = 5, size of lhs = 4:
% 1.68/1.85 P_subtract-{F}(V0,V1,V1,V2), P_zero-{F}(V0,V3), element-{F}(V1,V0), V2 == V3 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #44: input, references = 7, size of lhs = 5:
% 1.68/1.85 element-{F}(V1,V0), P_subtract-{F}(V0,V2,V1,V3), P_subtract-{F}(V0,V2,V3,V4), element-{F}(V2,V0), V4 == V1 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #45: input, references = 4, size of lhs = 9:
% 1.68/1.85 morphism-{F}(V0,V1,V2), P_apply-{F}(V0,V3,V4), element-{F}(V3,V1), P_subtract-{F}(V1,V5,V3,V6), P_apply-{F}(V0,V6,V7), P_apply-{F}(V0,V5,V8), P_subtract-{F}(V2,V8,V4,V9), element-{F}(V5,V1), V7 == V9 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #46: input, references = 8, size of lhs = 7:
% 1.68/1.85 injection_2-{F}(V0), P_zero-{F}(V1,V3), P_zero-{F}(V2,V4), morphism-{F}(V0,V2,V1), P_apply-{F}(V0,V5,V3), element-{F}(V5,V2), V5 == V4 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #47: input, references = 4, size of lhs = 3:
% 1.68/1.85 P_zero-{F}(V1,V3), P_zero-{F}(V2,V4), morphism-{F}(V0,V2,V1) | injection_2-{T}(V0), pppp17-{T}(V0,V2,V3,V4)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #48: input, references = 4, size of lhs = 1:
% 1.68/1.85 pppp17-{F}(V0,V1,V2,V3) | EXISTS V4: pppp12-{T}(V0,V1,V4,V2,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #49: input, references = 4, size of lhs = 2:
% 1.68/1.85 pppp12-{F}(V0,V1,V4,V3,V4), P_apply-{F}(V0,V4,V5) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #50: input, references = 4, size of lhs = 3:
% 1.68/1.85 pppp12-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V0,V2,V5), V5 == V3 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #51: input, references = 4, size of lhs = 2:
% 1.68/1.85 pppp12-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V0,V2,V5) | element-{T}(V2,V1)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #52: input, references = 4, size of lhs = 3:
% 1.68/1.85 P_x-{F}(V0), P_any1-{F}(V1), P_any2-{F}(V2) | morphism-{T}(V0,V1,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #53: input, references = 4, size of lhs = 3:
% 1.68/1.85 P_x-{F}(V0), P_any1-{F}(V1), P_any2-{F}(V2) | injection-{T}(V0), injection_2-{T}(V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #54: input, references = 6, size of lhs = 5:
% 1.68/1.85 P_x-{F}(V0), P_any1-{F}(V1), P_any2-{F}(V2), injection_2-{F}(V0), injection-{F}(V0) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #55: input, references = 12, size of lhs = 2:
% 1.68/1.85 #-{F} V0, #-{F} V1 | EXISTS V2: P_apply-{T}(V0,V1,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #56: input, references = 6, size of lhs = 1:
% 1.68/1.85 #-{F} V0 | EXISTS V1: P_zero-{T}(V0,V1)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #57: input, references = 7, size of lhs = 3:
% 1.68/1.85 #-{F} V0, #-{F} V1, #-{F} V2 | EXISTS V3: P_subtract-{T}(V0,V1,V2,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #58: input, references = 4, size of lhs = 0:
% 1.68/1.85 FALSE | EXISTS V0: P_x-{T}(V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #59: input, references = 4, size of lhs = 0:
% 1.68/1.85 FALSE | EXISTS V0: P_any1-{T}(V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #60: input, references = 4, size of lhs = 0:
% 1.68/1.85 FALSE | EXISTS V0: P_any2-{T}(V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 number of initial rules = 61
% 1.68/1.85
% 1.68/1.85 Simplifiers:
% 1.68/1.85 #61: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 morphism-{F}(V0,V1,V2), morphism-{F}(V3,V4,V5), V0 == V3 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #62: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 morphism-{F}(V0,V1,V2), morphism-{F}(V3,V4,V5), V1 == V4 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #63: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 morphism-{F}(V0,V1,V2), morphism-{F}(V3,V4,V5), V2 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #64: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 injection-{F}(V0), injection-{F}(V1), V0 == V1 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #65: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 surjection-{F}(V0), surjection-{F}(V1), V0 == V1 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #66: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 exact-{F}(V0,V1), V1 == V0 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #67: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 exact-{F}(V0,V1), exact-{F}(V2,V3), V0 == V2 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #68: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 commute-{F}(V0,V1,V2,V3), V1 == V0 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #69: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 commute-{F}(V0,V1,V2,V3), V2 == V0 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #70: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 commute-{F}(V0,V1,V2,V3), V3 == V0 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #71: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 commute-{F}(V0,V1,V2,V3), commute-{F}(V4,V5,V6,V7), V0 == V4 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #72: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 injection_2-{F}(V0), injection_2-{F}(V1), V0 == V1 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #73: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 P_apply-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #74: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 P_zero-{F}(V0,V1), P_zero-{F}(V0,V3), V1 == V3 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #75: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 P_subtract-{F}(V0,V1,V2,V3), P_subtract-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #76: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 P_x-{F}(V0), P_x-{F}(V1), V0 == V1 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #77: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 P_any1-{F}(V0), P_any1-{F}(V1), V0 == V1 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #78: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 P_any2-{F}(V0), P_any2-{F}(V1), V0 == V1 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #79: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp4-{F}(V0,V1,V2,V3,V4), pppp4-{F}(V0,V1,V7,V3,V4), V2 == V7 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #80: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp4-{F}(V0,V1,V2,V3,V4), pppp4-{F}(V0,V1,V7,V8,V9), V3 == V8 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #81: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp4-{F}(V0,V1,V2,V3,V4), pppp4-{F}(V5,V6,V7,V8,V9), V0 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #82: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp4-{F}(V0,V1,V2,V3,V4), pppp4-{F}(V5,V6,V7,V8,V9), V1 == V6 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #83: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp4-{F}(V0,V1,V2,V3,V4), pppp4-{F}(V0,V6,V7,V3,V9), V4 == V9 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #84: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp5-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #85: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp5-{F}(V0,V1,V2), pppp5-{F}(V3,V4,V5), V0 == V3 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #86: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp5-{F}(V0,V1,V2), pppp5-{F}(V3,V4,V5), V1 == V4 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #87: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp6-{F}(V0,V1,V2,V3), pppp6-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #88: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp6-{F}(V0,V1,V2,V3), pppp6-{F}(V4,V5,V6,V7), V0 == V4 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #89: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp6-{F}(V0,V1,V2,V3), pppp6-{F}(V4,V5,V6,V7), V1 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #90: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp7-{F}(V0,V1,V2,V3), pppp7-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #91: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp7-{F}(V0,V1,V2,V3), pppp7-{F}(V4,V5,V6,V7), V0 == V4 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #92: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp7-{F}(V0,V1,V2,V3), pppp7-{F}(V4,V5,V6,V7), V1 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #93: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp7-{F}(V0,V1,V2,V3), pppp7-{F}(V4,V5,V6,V7), V2 == V6 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #94: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp8-{F}(V0,V1,V2,V3), pppp8-{F}(V0,V5,V2,V3), V1 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #95: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp9-{F}(V0,V1,V2,V3,V4,V5), V3 == V2 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #96: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp9-{F}(V0,V1,V2,V3,V4,V5), V4 == V0 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #97: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp9-{F}(V0,V1,V2,V3,V4,V5), V1 == V0 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #98: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp9-{F}(V0,V1,V2,V3,V4,V5), pppp9-{F}(V0,V7,V2,V9,V10,V11), V5 == V11 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #99: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp9-{F}(V0,V1,V2,V3,V4,V5), pppp9-{F}(V6,V7,V8,V9,V10,V11), V2 == V8 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #100: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp9-{F}(V0,V1,V2,V3,V4,V5), pppp9-{F}(V6,V7,V8,V9,V10,V11), V0 == V6 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #101: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp9-{F}(V0,V1,V2,V3,V4,V5), pppp9-{F}(V6,V7,V8,V9,V10,V11), V0 == V6 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #102: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp10-{F}(V0,V1,V2,V3), pppp10-{F}(V0,V5,V2,V3), V1 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #103: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp11-{F}(V0,V1,V2,V3,V4,V5), V3 == V2 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #104: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp11-{F}(V0,V1,V2,V3,V4,V5), V4 == V2 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #105: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp11-{F}(V0,V1,V2,V3,V4,V5), V5 == V2 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #106: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp11-{F}(V0,V1,V2,V3,V4,V5), pppp11-{F}(V0,V7,V2,V9,V10,V11), V1 == V7 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #107: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp11-{F}(V0,V1,V2,V3,V4,V5), pppp11-{F}(V6,V7,V8,V9,V10,V11), V2 == V8 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #108: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp11-{F}(V0,V1,V2,V3,V4,V5), pppp11-{F}(V6,V7,V8,V9,V10,V11), V0 == V6 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #109: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V7,V3,V4), V2 == V7 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #110: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V5,V1,V7,V8,V9), V4 == V9 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #111: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V5,V6,V7,V8,V9), V0 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #112: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V5,V6,V7,V8,V9), V1 == V6 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #113: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp13-{F}(V0,V1), pppp13-{F}(V2,V3), V0 == V2 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #114: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp13-{F}(V0,V1), pppp13-{F}(V2,V3), V1 == V3 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #115: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp14-{F}(V0,V1,V2), pppp14-{F}(V3,V4,V5), V0 == V3 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #116: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp14-{F}(V0,V1,V2), pppp14-{F}(V3,V4,V5), V1 == V4 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #117: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp14-{F}(V0,V1,V2), pppp14-{F}(V3,V4,V5), V2 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #118: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp15-{F}(V0,V1,V2,V3,V4), V3 == V2 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #119: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp15-{F}(V0,V1,V2,V3,V4), V4 == V0 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #120: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp15-{F}(V0,V1,V2,V3,V4), V1 == V0 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #121: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp15-{F}(V0,V1,V2,V3,V4), pppp15-{F}(V5,V6,V7,V8,V9), V2 == V7 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #122: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp15-{F}(V0,V1,V2,V3,V4), pppp15-{F}(V5,V6,V7,V8,V9), V0 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #123: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp15-{F}(V0,V1,V2,V3,V4), pppp15-{F}(V5,V6,V7,V8,V9), V0 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #124: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp16-{F}(V0,V1,V2,V3,V4), V2 == V1 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #125: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp16-{F}(V0,V1,V2,V3,V4), V3 == V1 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #126: unsound, references = 3, size of lhs = 2:
% 1.68/1.85 pppp16-{F}(V0,V1,V2,V3,V4), V4 == V1 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #127: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp16-{F}(V0,V1,V2,V3,V4), pppp16-{F}(V5,V6,V7,V8,V9), V1 == V6 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #128: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp16-{F}(V0,V1,V2,V3,V4), pppp16-{F}(V5,V6,V7,V8,V9), V0 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #129: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V4,V1,V6,V7), V3 == V7 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #130: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V4,V5,V6,V7), V0 == V4 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #131: unsound, references = 3, size of lhs = 3:
% 1.68/1.85 pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V4,V5,V6,V7), V1 == V5 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 number of simplifiers = 71
% 1.68/1.85
% 1.68/1.85 Learnt:
% 1.68/1.85 #133: exists( #55, #1 ), references = 2, size of lhs = 3:
% 1.68/1.85 P_zero-{F}(V0,V1), morphism-{F}(V2,V0,V3), P_zero-{F}(V3,V4) | P_apply-{T}(V2,V1,V4)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #135: exists( #57, #43 ), references = 5, size of lhs = 2:
% 1.68/1.85 element-{F}(V0,V1), P_zero-{F}(V1,V2) | P_subtract-{T}(V1,V0,V0,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #149: mergings( V4 == V6; #146 ), references = 1, size of lhs = 4:
% 1.68/1.85 P_zero-{F}(V0,V1), P_subtract-{F}(V0,V1,V1,V2), V2 == V1, pppp5-{F}(V3,V0,V4) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #153: mergings( V3 == V5; #151 ), references = 1, size of lhs = 4:
% 1.68/1.85 pppp13-{F}(V0,V1), P_zero-{F}(V1,V2), P_subtract-{F}(V1,V2,V2,V3), V3 == V2 | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #156: mergings( V1 == V4; #154 ), references = 1, size of lhs = 2:
% 1.68/1.85 pppp13-{F}(V0,V1), P_zero-{F}(V1,V2) | P_subtract-{T}(V1,V2,V2,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #159: exists( #55, #50 ), references = 1, size of lhs = 1:
% 1.68/1.85 pppp12-{F}(V0,V1,V2,V3,V4) | P_apply-{T}(V0,V2,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #165: exists( #48, #163 ), references = 1, size of lhs = 5:
% 1.68/1.85 injection-{F}(V0), P_zero-{F}(V1,V2), P_apply-{F}(V0,V2,V3), pppp17-{F}(V0,V1,V3,V4), morphism-{F}(V0,V1,V5) | pppp12-{T}(V0,V1,V2,V3,V4)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #170: mergings( V0 == V5, V1 == V6; #167 ), references = 1, size of lhs = 5:
% 1.68/1.85 injection-{F}(V0), P_zero-{F}(V1,V2), morphism-{F}(V0,V1,V3), P_zero-{F}(V3,V4), P_apply-{F}(V0,V2,V4) | injection_2-{T}(V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #177: mergings( V6 == V9, V7 == V10, V1 == V3, V2 == V4; #172 ), references = 2, size of lhs = 7:
% 1.68/1.85 P_x-{F}(V0), P_any1-{F}(V1), P_any2-{F}(V2), P_zero-{F}(V3,V4), morphism-{F}(V0,V3,V5), P_zero-{F}(V5,V6), P_apply-{F}(V0,V4,V6) | injection_2-{T}(V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #181: exists( #55, #32 ), references = 3, size of lhs = 1:
% 1.68/1.85 pppp10-{F}(V0,V1,V2,V3) | P_apply-{T}(V2,V1,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #182: exists( #55, #11 ), references = 2, size of lhs = 1:
% 1.68/1.85 pppp6-{F}(V0,V1,V2,V3) | P_apply-{T}(V0,V3,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #183: exists( #55, #35 ), references = 1, size of lhs = 2:
% 1.68/1.85 P_zero-{F}(V0,V1), pppp2-{F}(V0,V2,V3,V4) | P_apply-{T}(V2,V4,V1)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #187: exists( #30, #185 ), references = 1, size of lhs = 5:
% 1.68/1.85 injection_2-{F}(V0), pppp3-{F}(V1,V0,V2), P_zero-{F}(V1,V3), morphism-{F}(V0,V1,V4), P_zero-{F}(V4,V2) | pppp10-{T}(V1,V3,V0,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #189: exists( #57, #44 ), references = 2, size of lhs = 3:
% 1.68/1.85 element-{F}(V0,V1), element-{F}(V2,V1), P_subtract-{F}(V1,V2,V0,V3) | P_subtract-{T}(V1,V2,V3,V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #194: mergings( V3 == V2, V4 == V0, V1 == V0; #190 ), references = 1, size of lhs = 4:
% 1.68/1.85 P_zero-{F}(V0,V1), pppp9-{F}(V0,V0,V2,V2,V0,V3), P_apply-{F}(V2,V3,V4), V4 == V1 | pppp3-{T}(V0,V2,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #200: mergings( V2 == V6; #198 ), references = 1, size of lhs = 6:
% 1.68/1.85 surjection-{F}(V0), injection_2-{F}(V0), P_zero-{F}(V1,V2), morphism-{F}(V0,V1,V3), P_zero-{F}(V3,V4), element-{F}(V4,V3) | pppp6-{T}(V0,V1,V4,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #204: exists( #55, #21 ), references = 2, size of lhs = 1:
% 1.68/1.85 pppp8-{F}(V0,V1,V2,V3) | P_apply-{T}(V2,V1,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #208: exists( #19, #206 ), references = 1, size of lhs = 5:
% 1.68/1.85 injection_2-{F}(V0), pppp1-{F}(V1,V0,V2), P_zero-{F}(V1,V3), morphism-{F}(V0,V1,V4), P_zero-{F}(V4,V2) | pppp8-{T}(V1,V3,V0,V2)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #213: exists( #55, #45 ), references = 1, size of lhs = 7:
% 1.68/1.85 element-{F}(V0,V1), element-{F}(V2,V1), P_subtract-{F}(V1,V2,V0,V3), morphism-{F}(V4,V1,V5), P_apply-{F}(V4,V0,V6), P_apply-{F}(V4,V2,V7), P_subtract-{F}(V5,V7,V6,V8) | P_apply-{T}(V4,V3,V8)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #218: mergings( V6 == V8; #216 ), references = 3, size of lhs = 9:
% 1.68/1.85 injection_2-{F}(V0), element-{F}(V1,V2), P_zero-{F}(V2,V3), element-{F}(V4,V2), morphism-{F}(V0,V2,V5), P_zero-{F}(V5,V6), P_apply-{F}(V0,V1,V7), P_apply-{F}(V0,V4,V8), P_subtract-{F}(V5,V8,V7,V6) | P_subtract-{T}(V2,V4,V1,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #224: mergings( V6 == V8; #222 ), references = 1, size of lhs = 9:
% 1.68/1.85 injection_2-{F}(V0), element-{F}(V1,V2), pppp3-{F}(V2,V0,V3), P_zero-{F}(V2,V4), morphism-{F}(V0,V2,V5), P_zero-{F}(V5,V6), P_apply-{F}(V0,V1,V7), P_subtract-{F}(V5,V7,V3,V6), P_subtract-{F}(V2,V1,V4,V8) | pppp10-{T}(V2,V8,V0,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #229: exists( #19, #227 ), references = 1, size of lhs = 9:
% 1.68/1.85 injection_2-{F}(V0), element-{F}(V1,V2), pppp1-{F}(V2,V0,V3), P_zero-{F}(V2,V4), morphism-{F}(V0,V2,V5), P_zero-{F}(V5,V6), P_apply-{F}(V0,V1,V7), P_subtract-{F}(V5,V7,V3,V6), P_subtract-{F}(V2,V1,V4,V8) | pppp8-{T}(V2,V8,V0,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #238: mergings( V3 == V2, V4 == V0, V1 == V0; #234 ), references = 1, size of lhs = 8:
% 1.68/1.85 injection_2-{F}(V0), P_zero-{F}(V1,V2), pppp9-{F}(V1,V1,V0,V0,V1,V3), element-{F}(V3,V4), morphism-{F}(V0,V4,V5), P_zero-{F}(V5,V2), P_zero-{F}(V4,V6), V3 == V6 | pppp3-{T}(V1,V0,V3)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #242: exists( #55, #8 ), references = 1, size of lhs = 1:
% 1.68/1.85 pppp4-{F}(V0,V1,V2,V3,V4) | P_apply-{T}(V0,V2,V4)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #247: exists( #5, #245 ), references = 2, size of lhs = 10:
% 1.68/1.85 injection_2-{F}(V0), element-{F}(V1,V2), pppp5-{F}(V0,V2,V3), P_apply-{F}(V0,V3,V4), P_zero-{F}(V2,V5), morphism-{F}(V0,V2,V6), P_zero-{F}(V6,V7), P_apply-{F}(V0,V1,V8), P_subtract-{F}(V6,V8,V4,V7), P_subtract-{F}(V2,V1,V5,V9) | pppp4-{T}(V0,V2,V9,V3,V4)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #265: mergings( V4 == V9, V7 == V8; #262 ), references = 1, size of lhs = 6:
% 1.68/1.85 injection_2-{F}(V0), morphism-{F}(V0,V1,V2), P_zero-{F}(V2,V3), pppp5-{F}(V0,V1,V4), P_zero-{F}(V1,V5), P_apply-{F}(V0,V5,V6) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #269: mergings( V3 == V8, V6 == V7; #266 ), references = 1, size of lhs = 6:
% 1.68/1.85 injection_2-{F}(V0), pppp13-{F}(V0,V1), morphism-{F}(V0,V1,V2), P_zero-{F}(V2,V3), P_zero-{F}(V1,V4), P_apply-{F}(V0,V4,V5) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #274: mergings( V2 == V4, V3 == V8, V6 == V7; #270 ), references = 2, size of lhs = 5:
% 1.68/1.85 injection_2-{F}(V0), morphism-{F}(V0,V1,V2), P_zero-{F}(V2,V3), P_zero-{F}(V1,V4), P_apply-{F}(V0,V4,V5) | injection-{T}(V0)
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #285: mergings( V0 == V9, V9 == V10, V2 == V4, V4 == V7, V3 == V5, V5 == V8; #278 ), references = 1, size of lhs = 4:
% 1.68/1.85 P_x-{F}(V0), P_any1-{F}(V1), P_any2-{F}(V2), morphism-{F}(V0,V3,V3) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #295: mergings( V7 == V9, V9 == V10, V2 == V5, V3 == V6; #290 ), references = 1, size of lhs = 5:
% 1.68/1.85 P_x-{F}(V0), P_any1-{F}(V1), P_any2-{F}(V2), P_zero-{F}(V3,V4), morphism-{F}(V0,V3,V5) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #299: mergings( V2 == V5, V3 == V6; #296 ), references = 1, size of lhs = 4:
% 1.68/1.85 P_x-{F}(V0), P_any1-{F}(V1), P_any2-{F}(V2), morphism-{F}(V0,V3,V4) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #304: mergings( V1 == V2, V2 == V4; #301 ), references = 1, size of lhs = 2:
% 1.68/1.85 P_x-{F}(V0), P_any1-{F}(V1) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #306: exists( #59, #301 ), references = 1, size of lhs = 1:
% 1.68/1.85 P_x-{F}(V0) | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 #308: exists( #58, #305 ), references = 1, size of lhs = 0:
% 1.68/1.85 FALSE | FALSE
% 1.68/1.85 (used 0 times, uses = {})
% 1.68/1.85
% 1.68/1.85 number of learnt formulas = 34
% 1.68/1.85
% 1.68/1.85
% 1.68/1.85 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.68/1.85
% 1.68/1.85 randbase = 1
%------------------------------------------------------------------------------