%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SWX228-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% 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 07:01:17 PM UTC 2026
% Result : Unsatisfiable 58.44s 58.68s
% Output : Refutation 58.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX228-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 12:56:08 EDT 2026
% 0.16/0.34 % CPUTime :
% 58.44/58.68 GeoParameters:
% 58.44/58.68
% 58.44/58.68 tptp_input = 1
% 58.44/58.68 tptp_output = 0
% 58.44/58.68 nonempty = 1
% 58.44/58.68 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 58.44/58.68 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 58.44/58.68
% 58.44/58.68
% 58.44/58.68 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 58.44/58.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 58.44/58.68
% 58.44/58.68 RuleSystem INPUT:
% 58.44/58.68
% 58.44/58.68 Initial Rules:
% 58.44/58.68 #0: input, references = 5, size of lhs = 4:
% 58.44/58.68 P_btrue-{F}(V0), P_aux-{F}(V1,V2,V3,V0,V4), P_union-{F}(V3,V1,V5), V4 == V5 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #1: input, references = 6, size of lhs = 6:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_aux-{F}(V2,V3,V4,V1,V5), P_union-{F}(V4,V2,V6), P_cons-{F}(V3,V6,V7), V5 == V7 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #2: input, references = 4, size of lhs = 4:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_barbar-{F}(V0,V2,V3), V3 == V0 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #3: input, references = 4, size of lhs = 4:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_barbar-{F}(V1,V2,V3), V3 == V2 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #4: input, references = 5, size of lhs = 7:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_s-{F}(V2,V4), P_s-{F}(V3,V5), P_eqNat-{F}(V4,V5,V6), P_eqNat-{F}(V2,V3,V7), V6 == V7 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #5: input, references = 4, size of lhs = 6:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_s-{F}(V3,V4), P_eqNat-{F}(V4,V2,V5), V5 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #6: input, references = 4, size of lhs = 6:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_s-{F}(V3,V4), P_eqNat-{F}(V2,V4,V5), V5 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #7: input, references = 4, size of lhs = 5:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), V3 == V0 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #8: input, references = 4, size of lhs = 7:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_elem-{F}(V5,V4,V6), V6 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #9: input, references = 8, size of lhs = 11:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_cons-{F}(V5,V6,V8), P_elem-{F}(V7,V8,V9), P_eqNat-{F}(V7,V5,V10), P_elem-{F}(V7,V6,V11), P_barbar-{F}(V10,V11,V12), V9 == V12 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #10: input, references = 4, size of lhs = 7:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_union-{F}(V4,V5,V6), V6 == V5 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #11: input, references = 6, size of lhs = 10:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_cons-{F}(V6,V7,V8), P_union-{F}(V8,V5,V9), P_elem-{F}(V6,V5,V10), P_aux-{F}(V5,V6,V7,V10,V11), V9 == V11 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #12: input, references = 13, size of lhs = 10:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_prop_union_comm-{F}(V6,V5,V7), P_union-{F}(V6,V5,V8), P_union-{F}(V5,V6,V9), P_eq-{F}(V8,V9,V10), V7 == V10 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #13: input, references = 4, size of lhs = 7:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), V5 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #14: input, references = 4, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), V6 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #15: input, references = 4, size of lhs = 12:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_s-{F}(V8,V9), P_s-{F}(V7,V10), P_eq2-{F}(V9,V10,V11), P_eq2-{F}(V8,V7,V12), V11 == V12 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #16: input, references = 4, size of lhs = 10:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_s-{F}(V7,V8), P_eq2-{F}(V8,V2,V9), V9 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #17: input, references = 4, size of lhs = 10:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_s-{F}(V7,V8), P_eq2-{F}(V2,V8,V9), V9 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #18: input, references = 4, size of lhs = 9:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_eq-{F}(V7,V7,V8), V8 == V0 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #19: input, references = 4, size of lhs = 9:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_eq2-{F}(V7,V7,V8), V8 == V0 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #20: input, references = 4, size of lhs = 9:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_eq3-{F}(V7,V7,V8), V8 == V0 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #21: input, references = 4, size of lhs = 12:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_eq2-{F}(V8,V7,V1), P_cons-{F}(V8,V11,V12), P_cons-{F}(V7,V10,V13), P_eq-{F}(V12,V13,V14), V14 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #22: input, references = 5, size of lhs = 13:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_eq2-{F}(V8,V7,V0), P_cons-{F}(V8,V11,V12), P_cons-{F}(V7,V10,V13), P_eq-{F}(V12,V13,V14), P_eq-{F}(V11,V10,V15), V14 == V15 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #23: input, references = 4, size of lhs = 10:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_cons-{F}(V8,V7,V9), P_eq-{F}(V4,V9,V10), V10 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #24: input, references = 4, size of lhs = 10:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_cons-{F}(V8,V7,V9), P_eq-{F}(V9,V4,V10), V10 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #25: input, references = 4, size of lhs = 9:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_prop_union_comm-{F}(V8,V7,V9), P_eq3-{F}(V9,V1,V0) | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #26: input, references = 6, size of lhs = 4:
% 58.44/58.68 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3 | EXISTS V4: P_aux-{T}(V0,V1,V2,V3,V4)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #27: input, references = 4, size of lhs = 0:
% 58.44/58.68 FALSE | EXISTS V0: P_btrue-{T}(V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #28: input, references = 9, size of lhs = 2:
% 58.44/58.68 #-{F} V0, #-{F} V1 | EXISTS V2: P_union-{T}(V0,V1,V2)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #29: input, references = 4, size of lhs = 0:
% 58.44/58.68 FALSE | EXISTS V0: P_bfalse-{T}(V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #30: input, references = 6, size of lhs = 2:
% 58.44/58.68 #-{F} V0, #-{F} V1 | EXISTS V2: P_cons-{T}(V0,V1,V2)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #31: input, references = 5, size of lhs = 2:
% 58.44/58.68 #-{F} V0, #-{F} V1 | EXISTS V2: P_barbar-{T}(V0,V1,V2)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #32: input, references = 8, size of lhs = 2:
% 58.44/58.68 #-{F} V0, #-{F} V1 | EXISTS V2: P_eqNat-{T}(V0,V1,V2)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #33: input, references = 3, size of lhs = 1:
% 58.44/58.68 #-{F} V0 | EXISTS V1: P_s-{T}(V0,V1)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #34: input, references = 4, size of lhs = 0:
% 58.44/58.68 FALSE | EXISTS V0: P_z-{T}(V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #35: input, references = 11, size of lhs = 2:
% 58.44/58.68 #-{F} V0, #-{F} V1 | EXISTS V2: P_elem-{T}(V0,V1,V2)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #36: input, references = 4, size of lhs = 0:
% 58.44/58.68 FALSE | EXISTS V0: P_nil-{T}(V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #37: input, references = 6, size of lhs = 2:
% 58.44/58.68 #-{F} V0, #-{F} V1 | EXISTS V2: P_prop_union_comm-{T}(V0,V1,V2)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #38: input, references = 16, size of lhs = 2:
% 58.44/58.68 #-{F} V0, #-{F} V1 | EXISTS V2: P_eq-{T}(V0,V1,V2)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #39: input, references = 6, size of lhs = 2:
% 58.44/58.68 #-{F} V0, #-{F} V1 | EXISTS V2: P_eq3-{T}(V0,V1,V2)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #40: input, references = 7, size of lhs = 2:
% 58.44/58.68 #-{F} V0, #-{F} V1 | EXISTS V2: P_eq2-{T}(V0,V1,V2)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 number of initial rules = 41
% 58.44/58.68
% 58.44/58.68 Simplifiers:
% 58.44/58.68 #41: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_aux-{F}(V0,V1,V2,V3,V4), P_aux-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #42: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_btrue-{F}(V0), P_btrue-{F}(V1), V0 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #43: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_union-{F}(V0,V1,V2), P_union-{F}(V0,V1,V5), V2 == V5 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #44: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_bfalse-{F}(V0), P_bfalse-{F}(V1), V0 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #45: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_cons-{F}(V0,V1,V2), P_cons-{F}(V0,V1,V5), V2 == V5 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #46: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_barbar-{F}(V0,V1,V2), P_barbar-{F}(V0,V1,V5), V2 == V5 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #47: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_eqNat-{F}(V0,V1,V2), P_eqNat-{F}(V0,V1,V5), V2 == V5 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #48: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_s-{F}(V0,V1), P_s-{F}(V0,V3), V1 == V3 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #49: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_z-{F}(V0), P_z-{F}(V1), V0 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #50: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_elem-{F}(V0,V1,V2), P_elem-{F}(V0,V1,V5), V2 == V5 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #51: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_nil-{F}(V0), P_nil-{F}(V1), V0 == V1 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #52: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_prop_union_comm-{F}(V0,V1,V2), P_prop_union_comm-{F}(V0,V1,V5), V2 == V5 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #53: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_eq-{F}(V0,V1,V2), P_eq-{F}(V0,V1,V5), V2 == V5 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #54: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_eq3-{F}(V0,V1,V2), P_eq3-{F}(V0,V1,V5), V2 == V5 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #55: unsound, references = 3, size of lhs = 3:
% 58.44/58.68 P_eq2-{F}(V0,V1,V2), P_eq2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 number of simplifiers = 15
% 58.44/58.68
% 58.44/58.68 Learnt:
% 58.44/58.68 #57: exists( #31, #3 ), references = 2, size of lhs = 3:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), #-{F} V2 | P_barbar-{T}(V1,V2,V2)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #61: exists( #32, #7 ), references = 2, size of lhs = 3:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2) | P_eqNat-{T}(V2,V2,V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #62: exists( #32, #10 ), references = 2, size of lhs = 6:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_nil-{F}(V3), P_union-{F}(V3,V4,V5), V5 == V4 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #65: exists( #28, #62 ), references = 3, size of lhs = 5:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_nil-{F}(V3), #-{F} V4 | P_union-{T}(V3,V4,V4)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #67: exists( #35, #8 ), references = 1, size of lhs = 6:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), #-{F} V5 | P_elem-{T}(V5,V4,V1)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #69: exists( #38, #12 ), references = 3, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_prop_union_comm-{F}(V5,V6,V7), P_union-{F}(V5,V6,V8), P_union-{F}(V6,V5,V9) | P_eq-{T}(V8,V9,V7)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #71: exists( #32, #6 ), references = 1, size of lhs = 4:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_s-{F}(V3,V4) | P_eqNat-{T}(V2,V4,V1)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #73: exists( #31, #2 ), references = 2, size of lhs = 3:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), #-{F} V2 | P_barbar-{T}(V0,V2,V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #75: exists( #38, #12 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_prop_union_comm-{F}(V5,V6,V7), P_union-{F}(V5,V6,V8), P_union-{F}(V6,V5,V9) | P_eq-{T}(V8,V9,V7)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #77: exists( #32, #4 ), references = 1, size of lhs = 5:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_s-{F}(V2,V3), P_s-{F}(V4,V5), P_eqNat-{F}(V2,V4,V6) | P_eqNat-{T}(V3,V5,V6)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #82: mergings( V3 == V5, V4 == V6; #79 ), references = 6, size of lhs = 9:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eqNat-{F}(V5,V6,V0), P_cons-{F}(V6,V7,V8), P_elem-{F}(V5,V8,V9), V9 == V0 | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #84: exists( #32, #5 ), references = 1, size of lhs = 4:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_s-{F}(V3,V4) | P_eqNat-{T}(V4,V2,V1)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #87: exists( #35, #82 ), references = 3, size of lhs = 7:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eqNat-{F}(V5,V6,V0), P_cons-{F}(V6,V7,V8) | P_elem-{T}(V5,V8,V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #88: exists( #35, #9 ), references = 1, size of lhs = 9:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_cons-{F}(V5,V6,V7), P_eqNat-{F}(V8,V5,V9), P_elem-{F}(V8,V6,V10), P_barbar-{F}(V9,V10,V11) | P_elem-{T}(V8,V7,V11)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #90: exists( #26, #0 ), references = 4, size of lhs = 3:
% 58.44/58.68 P_btrue-{F}(V0), P_union-{F}(V1,V2,V3), #-{F} V4 | P_aux-{T}(V2,V4,V1,V0,V3)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #92: exists( #32, #4 ), references = 1, size of lhs = 5:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_s-{F}(V2,V3), P_s-{F}(V4,V5), P_eqNat-{F}(V3,V5,V6) | P_eqNat-{T}(V2,V4,V6)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #94: exists( #37, #12 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_union-{F}(V5,V6,V7), P_union-{F}(V6,V5,V8), P_eq-{F}(V7,V8,V9) | P_prop_union_comm-{T}(V5,V6,V9)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #97: exists( #35, #82 ), references = 1, size of lhs = 7:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eqNat-{F}(V5,V6,V0), P_cons-{F}(V6,V7,V8) | P_elem-{T}(V5,V8,V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #98: exists( #35, #9 ), references = 1, size of lhs = 9:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_cons-{F}(V5,V6,V7), P_eqNat-{F}(V8,V5,V9), P_elem-{F}(V8,V6,V10), P_barbar-{F}(V9,V10,V11) | P_elem-{T}(V8,V7,V11)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #101: exists( #28, #11 ), references = 4, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_cons-{F}(V5,V6,V7), P_elem-{F}(V5,V8,V9), P_aux-{F}(V8,V5,V6,V9,V10) | P_union-{T}(V7,V8,V10)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #104: exists( #26, #11 ), references = 2, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_cons-{F}(V5,V6,V7), P_union-{F}(V7,V8,V9), P_elem-{F}(V5,V8,V10) | P_aux-{T}(V8,V5,V6,V10,V9)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #107: exists( #38, #12 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_prop_union_comm-{F}(V5,V6,V7), P_union-{F}(V5,V6,V8), P_union-{F}(V6,V5,V9) | P_eq-{T}(V8,V9,V7)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #112: mergings( V3 == V8, V4 == V9; #109 ), references = 1, size of lhs = 9:
% 58.44/58.68 P_z-{F}(V0), P_eqNat-{F}(V0,V0,V1), P_nil-{F}(V2), P_btrue-{F}(V3), P_bfalse-{F}(V4), P_elem-{F}(V5,V6,V4), P_cons-{F}(V5,V7,V8), P_union-{F}(V7,V6,V9), P_cons-{F}(V5,V9,V10) | P_union-{T}(V8,V6,V10)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #114: exists( #38, #12 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_prop_union_comm-{F}(V5,V6,V7), P_union-{F}(V5,V6,V8), P_union-{F}(V6,V5,V9) | P_eq-{T}(V8,V9,V7)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #116: exists( #35, #82 ), references = 1, size of lhs = 7:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eqNat-{F}(V5,V6,V0), P_cons-{F}(V6,V7,V8) | P_elem-{T}(V5,V8,V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #122: exists( #35, #82 ), references = 1, size of lhs = 7:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eqNat-{F}(V5,V6,V0), P_cons-{F}(V6,V7,V8) | P_elem-{T}(V5,V8,V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #124: exists( #30, #1 ), references = 1, size of lhs = 4:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_union-{F}(V2,V3,V4), P_aux-{F}(V3,V5,V2,V1,V6) | P_cons-{T}(V5,V4,V6)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #130: exists( #38, #12 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_prop_union_comm-{F}(V5,V6,V7), P_union-{F}(V5,V6,V8), P_union-{F}(V6,V5,V9) | P_eq-{T}(V8,V9,V7)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #134: exists( #26, #1 ), references = 1, size of lhs = 4:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_union-{F}(V2,V3,V4), P_cons-{F}(V5,V4,V6) | P_aux-{T}(V3,V5,V2,V1,V6)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #136: exists( #38, #12 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_prop_union_comm-{F}(V5,V6,V7), P_union-{F}(V5,V6,V8), P_union-{F}(V6,V5,V9) | P_eq-{T}(V8,V9,V7)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #140: exists( #28, #0 ), references = 1, size of lhs = 2:
% 58.44/58.68 P_btrue-{F}(V0), P_aux-{F}(V1,V2,V3,V0,V4) | P_union-{T}(V3,V1,V4)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #150: exists( #39, #13 ), references = 1, size of lhs = 5:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4) | P_eq3-{T}(V1,V0,V1)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #152: exists( #38, #12 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_prop_union_comm-{F}(V5,V6,V7), P_union-{F}(V5,V6,V8), P_union-{F}(V6,V5,V9) | P_eq-{T}(V8,V9,V7)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #154: exists( #38, #12 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_prop_union_comm-{F}(V5,V6,V7), P_union-{F}(V5,V6,V8), P_union-{F}(V6,V5,V9) | P_eq-{T}(V8,V9,V7)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #158: exists( #39, #14 ), references = 1, size of lhs = 6:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5) | P_eq3-{T}(V0,V1,V1)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #160: exists( #38, #18 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), #-{F} V7 | P_eq-{T}(V7,V7,V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #162: exists( #39, #20 ), references = 2, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), #-{F} V7 | P_eq3-{T}(V7,V7,V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #164: exists( #40, #19 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), #-{F} V7 | P_eq2-{T}(V7,V7,V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #166: exists( #38, #22 ), references = 1, size of lhs = 11:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_eq2-{F}(V7,V8,V0), P_cons-{F}(V7,V9,V10), P_cons-{F}(V8,V11,V12), P_eq-{F}(V10,V12,V13) | P_eq-{T}(V9,V11,V13)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #169: exists( #40, #15 ), references = 1, size of lhs = 10:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_s-{F}(V7,V8), P_s-{F}(V9,V10), P_eq2-{F}(V8,V10,V11) | P_eq2-{T}(V7,V9,V11)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #175: exists( #35, #82 ), references = 1, size of lhs = 7:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eqNat-{F}(V5,V6,V0), P_cons-{F}(V6,V7,V8) | P_elem-{T}(V5,V8,V0)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #176: exists( #35, #9 ), references = 1, size of lhs = 9:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_cons-{F}(V5,V6,V7), P_eqNat-{F}(V8,V5,V9), P_elem-{F}(V8,V6,V10), P_barbar-{F}(V9,V10,V11) | P_elem-{T}(V8,V7,V11)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #187: exists( #38, #23 ), references = 2, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_cons-{F}(V7,V8,V9) | P_eq-{T}(V4,V9,V1)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #189: exists( #38, #24 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_cons-{F}(V7,V8,V9) | P_eq-{T}(V9,V4,V1)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #191: exists( #40, #17 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_s-{F}(V7,V8) | P_eq2-{T}(V2,V8,V1)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #196: mergings( V3 == V5, V4 == V6; #193 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eqNat-{F}(V5,V6,V1), P_cons-{F}(V6,V7,V8), P_elem-{F}(V5,V8,V9) | P_elem-{T}(V5,V7,V9)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #198: exists( #40, #16 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_s-{F}(V7,V8) | P_eq2-{T}(V8,V2,V1)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #205: exists( #28, #11 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_cons-{F}(V5,V6,V7), P_elem-{F}(V5,V8,V9), P_aux-{F}(V8,V5,V6,V9,V10) | P_union-{T}(V7,V8,V10)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #207: exists( #38, #12 ), references = 1, size of lhs = 8:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_prop_union_comm-{F}(V5,V6,V7), P_union-{F}(V5,V6,V8), P_union-{F}(V6,V5,V9) | P_eq-{T}(V8,V9,V7)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #216: mergings( V3 == V8, V4 == V9, V5 == V10, V6 == V11, V7 == V12; #210 ), references = 1, size of lhs = 12:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_eq2-{F}(V7,V8,V1), P_cons-{F}(V7,V9,V10), P_union-{F}(V11,V12,V10), P_union-{F}(V12,V11,V13), P_cons-{F}(V8,V14,V13) | P_prop_union_comm-{T}(V11,V12,V1)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #227: mergings( V3 == V8, V4 == V9, V5 == V10, V6 == V11, V7 == V12; #221 ), references = 1, size of lhs = 13:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_eq2-{F}(V7,V8,V0), P_cons-{F}(V7,V9,V10), P_union-{F}(V11,V12,V10), P_union-{F}(V12,V11,V13), P_cons-{F}(V8,V14,V13), P_eq-{F}(V9,V14,V15) | P_prop_union_comm-{T}(V11,V12,V15)
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #242: mergings( V3 == V8, V8 == V15, V4 == V9, V9 == V16, V5 == V10, V6 == V11, V10 == V17, V11 == V18, V7 == V12, V12 == V19, V13 == V20, V14 == V21; #229 ), references = 2, size of lhs = 14:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_eq3-{F}(V7,V1,V0), P_eq2-{F}(V8,V9,V0), P_cons-{F}(V8,V10,V11), P_eq-{F}(V10,V12,V7), P_cons-{F}(V9,V12,V13), P_union-{F}(V14,V15,V11), P_union-{F}(V15,V14,V13) | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #271: mergings( V3 == V7, V7 == V12, V12 == V17, V17 == V22, V4 == V8, V8 == V13, V13 == V18, V18 == V23, V5 == V9, V9 == V14, V10 == V15, V14 == V19, V15 == V20, V19 == V24, V20 == V25, V6 == V11, V11 == V16, V16 == V21, V21 == V26; #251 ), references = 2, size of lhs = 15:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_eq3-{F}(V7,V1,V0), P_eqNat-{F}(V8,V9,V0), P_cons-{F}(V8,V4,V10), P_eq2-{F}(V11,V9,V0), P_elem-{F}(V9,V10,V12), P_eq-{F}(V13,V14,V7), P_cons-{F}(V11,V13,V15), P_aux-{F}(V10,V9,V14,V12,V15) | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #302: mergings( V3 == V10, V10 == V15, V15 == V21, V21 == V22, V4 == V6, V6 == V11, V11 == V16, V16 == V23, V5 == V7, V7 == V12, V8 == V13, V12 == V17, V13 == V18, V17 == V24, V18 == V25, V9 == V14, V14 == V1, V19 == V26, V20 == V27; #282 ), references = 1, size of lhs = 10:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_eq3-{F}(V1,V1,V0), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_nil-{F}(V4), P_eq3-{F}(V1,V0,V5), P_eq3-{F}(V0,V1,V6), P_eqNat-{F}(V7,V7,V0), P_eq2-{F}(V7,V7,V0) | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #329: mergings( V9 == V15, V15 == V21, V21 == V22, V10 == V12, V12 == V16, V16 == V23, V1 == V3, V2 == V4, V3 == V5, V4 == V6, V5 == V7, V6 == V8, V7 == V11, V11 == V13, V8 == V14, V13 == V17, V14 == V18, V17 == V19, V18 == V20, V19 == V24, V20 == V25; #307 ), references = 1, size of lhs = 5:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eqNat-{F}(V2,V2,V3), P_eqNat-{F}(V4,V4,V0) | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #338: mergings( V2 == V5, V5 == V7, V1 == V3, V3 == V4, V4 == V6, V6 == V8; #331 ), references = 1, size of lhs = 2:
% 58.44/58.68 P_btrue-{F}(V0), P_bfalse-{F}(V1) | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #342: mergings( V1 == V2, V2 == V3; #339 ), references = 1, size of lhs = 1:
% 58.44/58.68 P_btrue-{F}(V0) | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 #344: exists( #27, #339 ), references = 1, size of lhs = 0:
% 58.44/58.68 FALSE | FALSE
% 58.44/58.68 (used 0 times, uses = {})
% 58.44/58.68
% 58.44/58.68 number of learnt formulas = 58
% 58.44/58.68
% 58.44/58.68
% 58.44/58.68 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 58.44/58.68
% 58.44/58.68 randbase = 1
%------------------------------------------------------------------------------