TSTP Solution File: SEU238+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SEU238+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n007.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 06:17:35 EDT 2022
% Result : Theorem 16.41s 16.64s
% Output : Refutation 16.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU238+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n007.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 18:13:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 16.41/16.64 GeoParameters:
% 16.41/16.64
% 16.41/16.64 tptp_input = 1
% 16.41/16.64 tptp_output = 0
% 16.41/16.64 nonempty = 1
% 16.41/16.64 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.41/16.64 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 16.41/16.64
% 16.41/16.64
% 16.41/16.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.41/16.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.41/16.64
% 16.41/16.64 RuleSystem INPUT:
% 16.41/16.64
% 16.41/16.64 Initial Rules:
% 16.41/16.64 #0: input, references = 16, size of lhs = 2:
% 16.41/16.64 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #1: input, references = 4, size of lhs = 2:
% 16.41/16.64 proper_subset-{F}(V0,V1), proper_subset-{F}(V1,V0) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #2: input, references = 3, size of lhs = 1:
% 16.41/16.64 empty-{F}(V0) | function-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #3: input, references = 4, size of lhs = 1:
% 16.41/16.64 ordinal-{F}(V0) | epsilon_transitive-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #4: input, references = 3, size of lhs = 1:
% 16.41/16.64 ordinal-{F}(V0) | epsilon_connected-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #5: input, references = 3, size of lhs = 1:
% 16.41/16.64 empty-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #6: input, references = 3, size of lhs = 3:
% 16.41/16.64 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #7: input, references = 3, size of lhs = 2:
% 16.41/16.64 epsilon_transitive-{F}(V0), epsilon_connected-{F}(V0) | ordinal-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #8: input, references = 3, size of lhs = 1:
% 16.41/16.64 empty-{F}(V0) | epsilon_transitive-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #9: input, references = 3, size of lhs = 1:
% 16.41/16.64 empty-{F}(V0) | epsilon_connected-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #10: input, references = 3, size of lhs = 1:
% 16.41/16.64 empty-{F}(V0) | ordinal-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #11: input, references = 4, size of lhs = 3:
% 16.41/16.64 P_set_union2-{F}(V0,V1,V2), P_set_union2-{F}(V1,V0,V3), V2 == V3 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #12: input, references = 8, size of lhs = 2:
% 16.41/16.64 ordinal-{F}(V0), ordinal-{F}(V1) | ordinal_subset-{T}(V1,V0), ordinal_subset-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #13: input, references = 5, size of lhs = 4:
% 16.41/16.64 P_succ-{F}(V0,V1), P_singleton-{F}(V0,V2), P_set_union2-{F}(V0,V2,V3), V1 == V3 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #14: input, references = 3, size of lhs = 1:
% 16.41/16.64 proper_subset-{F}(V0,V1) | pppp0-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #15: input, references = 13, size of lhs = 1:
% 16.41/16.64 pppp0-{F}(V0,V1) | proper_subset-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #16: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp0-{F}(V0,V1) | subset-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #17: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp0-{F}(V1,V1) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #18: input, references = 13, size of lhs = 2:
% 16.41/16.64 subset-{F}(V0,V1), V0 == V1 | pppp0-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #19: input, references = 6, size of lhs = 1:
% 16.41/16.64 #-{F} V0 | EXISTS V1: pppp2-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #20: input, references = 8, size of lhs = 1:
% 16.41/16.64 pppp2-{F}(V0,V1) | element-{T}(V1,V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #21: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | empty-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #22: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #23: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #24: input, references = 3, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), empty-{F}(V2) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #25: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | empty-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #26: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | pppp3-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #27: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp3-{F}(V0) | ordinal-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #28: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp3-{F}(V0) | epsilon_connected-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #29: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp3-{F}(V0) | epsilon_transitive-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #30: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp3-{F}(V0) | empty-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #31: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp3-{F}(V0) | one_to_one-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #32: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp3-{F}(V0) | function-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #33: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp3-{F}(V0) | relation_empty_yielding-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #34: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp3-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #35: input, references = 3, size of lhs = 4:
% 16.41/16.64 P_empty_set-{F}(V0), relation-{F}(V1), P_set_union2-{F}(V2,V1,V3), relation-{F}(V2) | relation-{T}(V3)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #36: input, references = 3, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), P_set_union2-{F}(V1,V2,V3), empty-{F}(V3) | empty-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #37: input, references = 3, size of lhs = 4:
% 16.41/16.64 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), ordinal-{F}(V1), empty-{F}(V2) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #38: input, references = 4, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), ordinal-{F}(V1) | epsilon_transitive-{T}(V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #39: input, references = 3, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), ordinal-{F}(V1) | epsilon_connected-{T}(V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #40: input, references = 4, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), ordinal-{F}(V1) | ordinal-{T}(V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #41: input, references = 3, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), P_set_union2-{F}(V2,V1,V3), empty-{F}(V3) | empty-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #42: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | empty-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #43: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #44: input, references = 4, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), P_set_union2-{F}(V1,V1,V2), V2 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #45: input, references = 3, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), proper_subset-{F}(V1,V1) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #46: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp4-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #47: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp4-{F}(V0) | function-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #48: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp4-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #49: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp5-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #50: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp5-{F}(V0) | ordinal-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #51: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp5-{F}(V0) | epsilon_connected-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #52: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp5-{F}(V0) | epsilon_transitive-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #53: input, references = 4, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp6-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #54: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp6-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #55: input, references = 5, size of lhs = 1:
% 16.41/16.64 pppp6-{F}(V0) | empty-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #56: input, references = 4, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp7-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #57: input, references = 4, size of lhs = 1:
% 16.41/16.64 pppp7-{F}(V0) | empty-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #58: input, references = 4, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp8-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #59: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp8-{F}(V0) | function-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #60: input, references = 5, size of lhs = 1:
% 16.41/16.64 pppp8-{F}(V0) | empty-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #61: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp8-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #62: input, references = 4, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp10-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #63: input, references = 4, size of lhs = 1:
% 16.41/16.64 pppp10-{F}(V0) | pppp9-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #64: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp9-{F}(V0) | ordinal-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #65: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp9-{F}(V0) | epsilon_connected-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #66: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp9-{F}(V0) | epsilon_transitive-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #67: input, references = 4, size of lhs = 1:
% 16.41/16.64 pppp9-{F}(V0) | empty-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #68: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp9-{F}(V0) | one_to_one-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #69: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp9-{F}(V0) | function-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #70: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp9-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #71: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp11-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #72: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp11-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #73: input, references = 3, size of lhs = 2:
% 16.41/16.64 pppp11-{F}(V0), empty-{F}(V0) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #74: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp12-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #75: input, references = 3, size of lhs = 2:
% 16.41/16.64 pppp12-{F}(V0), empty-{F}(V0) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #76: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp13-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #77: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp13-{F}(V0) | one_to_one-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #78: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp13-{F}(V0) | function-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #79: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp13-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #80: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp14-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #81: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp14-{F}(V0) | ordinal-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #82: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp14-{F}(V0) | epsilon_connected-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #83: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp14-{F}(V0) | epsilon_transitive-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #84: input, references = 3, size of lhs = 2:
% 16.41/16.64 pppp14-{F}(V0), empty-{F}(V0) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #85: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp15-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #86: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp15-{F}(V0) | relation_empty_yielding-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #87: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp15-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #88: input, references = 3, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp16-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #89: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp16-{F}(V0) | function-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #90: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp16-{F}(V0) | relation_empty_yielding-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #91: input, references = 3, size of lhs = 1:
% 16.41/16.64 pppp16-{F}(V0) | relation-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #92: input, references = 17, size of lhs = 4:
% 16.41/16.64 P_empty_set-{F}(V0), ordinal-{F}(V1), ordinal-{F}(V2), ordinal_subset-{F}(V2,V1) | subset-{T}(V2,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #93: input, references = 3, size of lhs = 4:
% 16.41/16.64 P_empty_set-{F}(V0), ordinal-{F}(V1), ordinal-{F}(V2), subset-{F}(V2,V1) | ordinal_subset-{T}(V2,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #94: input, references = 3, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), ordinal-{F}(V1), ordinal-{F}(V2) | ordinal_subset-{T}(V2,V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #95: input, references = 3, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), #-{F} V1 | subset-{T}(V1,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #96: input, references = 5, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), P_succ-{F}(V1,V2) | in-{T}(V1,V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #97: input, references = 4, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), P_set_union2-{F}(V1,V0,V2), V2 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #98: input, references = 6, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #99: input, references = 11, size of lhs = 4:
% 16.41/16.64 P_empty_set-{F}(V0), epsilon_transitive-{F}(V1), ordinal-{F}(V2), proper_subset-{F}(V1,V2) | in-{T}(V1,V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #100: input, references = 6, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #101: input, references = 11, size of lhs = 5:
% 16.41/16.64 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), ordinal-{F}(V1), ordinal-{F}(V3), in-{F}(V1,V3) | ordinal_subset-{T}(V2,V3)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #102: input, references = 9, size of lhs = 5:
% 16.41/16.64 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), ordinal-{F}(V1), ordinal-{F}(V3), ordinal_subset-{F}(V2,V3) | in-{T}(V1,V3)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #103: input, references = 4, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3) | subset-{T}(V1,V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #104: input, references = 8, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), subset-{F}(V1,V2) | element-{T}(V1,V3)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #105: input, references = 4, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), ordinal-{F}(V1), being_limit_ordinal-{F}(V1) | pppp1-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #106: input, references = 4, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), ordinal-{F}(V1), pppp1-{F}(V1) | being_limit_ordinal-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #107: input, references = 8, size of lhs = 5:
% 16.41/16.64 P_empty_set-{F}(V0), pppp1-{F}(V1), P_succ-{F}(V2,V3), ordinal-{F}(V2), in-{F}(V2,V1) | in-{T}(V3,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #108: input, references = 7, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), #-{F} V1 | pppp1-{T}(V1), pppp21-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #109: input, references = 9, size of lhs = 1:
% 16.41/16.64 pppp21-{F}(V0) | EXISTS V1: pppp17-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #110: input, references = 7, size of lhs = 3:
% 16.41/16.64 pppp17-{F}(V0,V1), P_succ-{F}(V1,V2), in-{F}(V2,V0) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #111: input, references = 14, size of lhs = 2:
% 16.41/16.64 pppp17-{F}(V0,V1), P_succ-{F}(V1,V2) | in-{T}(V1,V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #112: input, references = 9, size of lhs = 2:
% 16.41/16.64 pppp17-{F}(V0,V1), P_succ-{F}(V1,V2) | ordinal-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #113: input, references = 4, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | EXISTS V1: pppp20-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #114: input, references = 4, size of lhs = 1:
% 16.41/16.64 pppp20-{F}(V0) | pppp19-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #115: input, references = 4, size of lhs = 3:
% 16.41/16.64 pppp19-{F}(V2), P_succ-{F}(V1,V2), ordinal-{F}(V1) | being_limit_ordinal-{T}(V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #116: input, references = 3, size of lhs = 3:
% 16.41/16.64 pppp19-{F}(V2), P_succ-{F}(V1,V2), ordinal-{F}(V1) | EXISTS V3: pppp18-{T}(V2,V3)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #117: input, references = 4, size of lhs = 2:
% 16.41/16.64 pppp19-{F}(V0), being_limit_ordinal-{F}(V0) | EXISTS V1: pppp18-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #118: input, references = 4, size of lhs = 1:
% 16.41/16.64 pppp19-{F}(V0) | ordinal-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #119: input, references = 4, size of lhs = 3:
% 16.41/16.64 pppp18-{F}(V0,V1), P_succ-{F}(V1,V2), V0 == V2 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #120: input, references = 5, size of lhs = 2:
% 16.41/16.64 pppp18-{F}(V0,V1), P_succ-{F}(V1,V2) | ordinal-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #121: input, references = 7, size of lhs = 4:
% 16.41/16.64 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3), in-{F}(V4,V1) | element-{T}(V4,V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #122: input, references = 6, size of lhs = 5:
% 16.41/16.64 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V1), element-{F}(V3,V2), in-{F}(V4,V3) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #123: input, references = 8, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #124: input, references = 4, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #125: input, references = 5, size of lhs = 4:
% 16.41/16.64 P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #126: input, references = 7, size of lhs = 2:
% 16.41/16.64 #-{F} V0, #-{F} V1 | EXISTS V2: P_set_union2-{T}(V0,V1,V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #127: input, references = 15, size of lhs = 1:
% 16.41/16.64 #-{F} V0 | EXISTS V1: P_succ-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #128: input, references = 4, size of lhs = 1:
% 16.41/16.64 #-{F} V0 | EXISTS V1: P_singleton-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #129: input, references = 4, size of lhs = 0:
% 16.41/16.64 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #130: input, references = 6, size of lhs = 1:
% 16.41/16.64 #-{F} V0 | EXISTS V1: P_powerset-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 number of initial rules = 131
% 16.41/16.64
% 16.41/16.64 Simplifiers:
% 16.41/16.64 #131: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 P_set_union2-{F}(V0,V1,V2), P_set_union2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #132: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 P_succ-{F}(V0,V1), P_succ-{F}(V0,V3), V1 == V3 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #133: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 P_singleton-{F}(V0,V1), P_singleton-{F}(V0,V3), V1 == V3 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #134: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #135: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 P_powerset-{F}(V0,V1), P_powerset-{F}(V0,V3), V1 == V3 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #136: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp2-{F}(V0,V1), pppp2-{F}(V0,V3), V1 == V3 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #137: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp3-{F}(V0), pppp3-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #138: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp4-{F}(V0), pppp4-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #139: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #140: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #141: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp7-{F}(V0), pppp7-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #142: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #143: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #144: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp10-{F}(V0), pppp10-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #145: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp11-{F}(V0), pppp11-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #146: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp12-{F}(V0), pppp12-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #147: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp13-{F}(V0), pppp13-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #148: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp14-{F}(V0), pppp14-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #149: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp15-{F}(V0), pppp15-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #150: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp16-{F}(V0), pppp16-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #151: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp17-{F}(V0,V1), pppp17-{F}(V0,V3), V1 == V3 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #152: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp18-{F}(V0,V1), pppp18-{F}(V0,V3), V1 == V3 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #153: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp18-{F}(V0,V1), pppp18-{F}(V2,V3), V0 == V2 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #154: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp19-{F}(V0), pppp19-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #155: unsound, references = 3, size of lhs = 3:
% 16.41/16.64 pppp20-{F}(V0), pppp20-{F}(V1), V0 == V1 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 number of simplifiers = 25
% 16.41/16.64
% 16.41/16.64 Learnt:
% 16.41/16.64 #158: exists( #126, #44 ), references = 1, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), #-{F} V1 | P_set_union2-{T}(V1,V1,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #164: mergings( V0 == V2; #162 ), references = 1, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | pppp7-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #170: mergings( V0 == V2; #167 ), references = 1, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | pppp6-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #172: mergings( V0 == V2; #168 ), references = 1, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), empty-{F}(V1) | pppp6-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #179: mergings( V0 == V2; #176 ), references = 1, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | pppp8-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #181: mergings( V0 == V2; #177 ), references = 1, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), empty-{F}(V1) | pppp8-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #190: mergings( V0 == V2; #188 ), references = 1, size of lhs = 1:
% 16.41/16.64 P_empty_set-{F}(V0) | pppp10-{T}(V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #198: exists( #126, #97 ), references = 2, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), #-{F} V1 | P_set_union2-{T}(V1,V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #200: exists( #126, #11 ), references = 2, size of lhs = 1:
% 16.41/16.64 P_set_union2-{F}(V0,V1,V2) | P_set_union2-{T}(V1,V0,V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #209: exists( #128, #207 ), references = 1, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), P_succ-{F}(V0,V1) | P_singleton-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #211: disj( #100, input ), references = 1, size of lhs = 2:
% 16.41/16.64 P_empty_set-{F}(V0), element-{F}(V1,V1) | empty-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #233: exists( #126, #13 ), references = 1, size of lhs = 2:
% 16.41/16.64 P_succ-{F}(V0,V1), P_singleton-{F}(V0,V2) | P_set_union2-{T}(V0,V2,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #249: disj( #100, input ), references = 3, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), element-{F}(V1,V2), in-{F}(V2,V1) | empty-{T}(V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #261: mergings( V0 == V2; #259 ), references = 2, size of lhs = 4:
% 16.41/16.64 P_empty_set-{F}(V0), ordinal-{F}(V1), P_succ-{F}(V1,V2), in-{F}(V1,V2) | pppp21-{T}(V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #284: mergings( V0 == V3; #280 ), references = 9, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), element-{F}(V1,V2), V2 == V0 | in-{T}(V1,V2)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #287: mergings( V0 == V3, V2 == V3; #281 ), references = 1, size of lhs = 4:
% 16.41/16.64 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, element-{F}(V2,V0) | in-{T}(V2,V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #289: mergings( V2 == V0; #282 ), references = 1, size of lhs = 3:
% 16.41/16.64 P_empty_set-{F}(V0), pppp12-{F}(V0), element-{F}(V1,V0) | in-{T}(V1,V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #401: mergings( V2 == V3, V3 == V4, V4 == V6; #397 ), references = 2, size of lhs = 7:
% 16.41/16.64 epsilon_transitive-{F}(V0), ordinal-{F}(V0), ordinal-{F}(V1), V0 == V1, P_succ-{F}(V0,V2), P_succ-{F}(V1,V2), P_empty_set-{F}(V3) | ordinal_subset-{T}(V1,V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #420: mergings( V2 == V3, V3 == V4; #417 ), references = 1, size of lhs = 8:
% 16.41/16.64 epsilon_transitive-{F}(V0), ordinal-{F}(V0), ordinal-{F}(V1), V0 == V1, pppp1-{F}(V1), P_empty_set-{F}(V2), P_succ-{F}(V0,V3), in-{F}(V1,V3) | ordinal_subset-{T}(V1,V0)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #431: mergings( V0 == V2, V2 == V3, V3 == V5, V5 == V7, V7 == V8, V8 == V9; #424 ), references = 1, size of lhs = 11:
% 16.41/16.64 epsilon_transitive-{F}(V0), ordinal-{F}(V0), ordinal-{F}(V1), V0 == V1, P_succ-{F}(V0,V2), in-{F}(V1,V2), P_empty_set-{F}(V3), empty-{F}(V4), P_powerset-{F}(V4,V5), P_powerset-{F}(V0,V5), in-{F}(V6,V1) | pppp21-{T}(V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #464: mergings( V2 == V3, V3 == V4; #461 ), references = 5, size of lhs = 7:
% 16.41/16.64 ordinal-{F}(V0), ordinal-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_powerset-{F}(V0,V4), in-{F}(V5,V1) | ordinal_subset-{T}(V0,V1)
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #498: mergings( V2 == V3, V3 == V6, V6 == V7, V7 == V9, V9 == V11, V11 == V12; #491 ), references = 2, size of lhs = 14:
% 16.41/16.64 empty-{F}(V0), P_powerset-{F}(V0,V1), epsilon_transitive-{F}(V2), P_powerset-{F}(V2,V1), ordinal-{F}(V2), ordinal-{F}(V3), V2 == V3, P_succ-{F}(V2,V4), V4 == V3, ordinal-{F}(V4), epsilon_transitive-{F}(V4), in-{F}(V3,V4), P_empty_set-{F}(V5), V3 == V5 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #506: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V9, V9 == V10; #499 ), references = 3, size of lhs = 12:
% 16.41/16.64 empty-{F}(V0), epsilon_transitive-{F}(V0), ordinal-{F}(V0), ordinal-{F}(V1), V0 == V1, P_succ-{F}(V0,V2), V2 == V1, ordinal-{F}(V2), epsilon_transitive-{F}(V2), in-{F}(V1,V2), P_empty_set-{F}(V3), V1 == V3 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #536: exists( #127, #530 ), references = 1, size of lhs = 12:
% 16.41/16.64 empty-{F}(V0), epsilon_transitive-{F}(V0), ordinal-{F}(V0), ordinal-{F}(V1), V0 == V1, P_succ-{F}(V0,V2), V2 == V1, pppp17-{F}(V2,V1), ordinal-{F}(V2), epsilon_transitive-{F}(V2), P_empty_set-{F}(V3), V1 == V3 | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #537: exists( #127, #531 ), references = 2, size of lhs = 2:
% 16.41/16.64 pppp17-{F}(V0,V1), in-{F}(V0,V1) | FALSE
% 16.41/16.64 (used 0 times, uses = {})
% 16.41/16.64
% 16.41/16.64 #538: exists( #127, #532 ), references = 1, size of lhs = 14:
% 16.41/16.64 empty-{F}(V0), P_powerset-{F}(V0,V1), epsilon_transitive-{F}(V2), P_powerset-{F}(V2,V1), ordinal-{F}(V2), ordinal-{F}(V3), V2 == V3, P_succ-{F}(V2,V4), V4 == V3, pppp17-{F}(V4,V3), ordinal-{F}(V4), epsilon_transitive-{F}(V4), P_empty_set-{F}(V5), V3 == V5 | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #543: exists( #127, #539 ), references = 1, size of lhs = 1:
% 16.41/16.65 pppp17-{F}(V0,V0) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #544: exists( #127, #540 ), references = 1, size of lhs = 2:
% 16.41/16.65 pppp17-{F}(V0,V1), pppp17-{F}(V1,V0) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #583: mergings( V2 == V3, V3 == V4; #580 ), references = 1, size of lhs = 6:
% 16.41/16.65 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), V1 == V0, pppp17-{F}(V2,V3), in-{F}(V1,V4), in-{F}(V4,V3) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #604: mergings( V2 == V3, V3 == V4, V4 == V6, V6 == V7; #599 ), references = 5, size of lhs = 4:
% 16.41/16.65 ordinal-{F}(V0), ordinal-{F}(V1), pppp17-{F}(V1,V0), P_empty_set-{F}(V2) | P_succ-{T}(V0,V1)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #639: disj( #12, #102+#0 ), references = 1, size of lhs = 4:
% 16.41/16.65 ordinal-{F}(V0), P_empty_set-{F}(V1), ordinal-{F}(V2), P_succ-{F}(V2,V0) | ordinal_subset-{T}(V2,V0)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #640: disj( #12, #102+#110 ), references = 1, size of lhs = 7:
% 16.41/16.65 ordinal-{F}(V0), P_empty_set-{F}(V1), ordinal-{F}(V2), P_succ-{F}(V2,V0), ordinal-{F}(V3), pppp17-{F}(V3,V4), P_succ-{F}(V4,V2) | ordinal_subset-{T}(V3,V0)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #700: disj( #12, #102+#0 ), references = 1, size of lhs = 6:
% 16.41/16.65 ordinal-{F}(V0), P_empty_set-{F}(V1), ordinal-{F}(V2), P_succ-{F}(V2,V0), ordinal-{F}(V3), in-{F}(V3,V2) | ordinal_subset-{T}(V3,V0)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #740: exists( #127, #737 ), references = 3, size of lhs = 12:
% 16.41/16.65 empty-{F}(V0), epsilon_transitive-{F}(V0), ordinal-{F}(V0), P_succ-{F}(V0,V1), ordinal-{F}(V1), epsilon_transitive-{F}(V1), pppp17-{F}(V1,V2), V0 == V2, V1 == V2, P_empty_set-{F}(V3), V2 == V3, pppp17-{F}(V4,V2) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #742: exists( #109, #739 ), references = 1, size of lhs = 8:
% 16.41/16.65 pppp21-{F}(V0), ordinal-{F}(V0), epsilon_transitive-{F}(V0), empty-{F}(V1), epsilon_transitive-{F}(V1), ordinal-{F}(V1), P_succ-{F}(V1,V0), P_empty_set-{F}(V2) | pppp17-{T}(V0,V1), pppp17-{T}(V0,V0), pppp17-{T}(V0,V2)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #799: exists( #109, #740 ), references = 1, size of lhs = 8:
% 16.41/16.65 pppp21-{F}(V0), ordinal-{F}(V0), epsilon_transitive-{F}(V0), empty-{F}(V1), epsilon_transitive-{F}(V1), ordinal-{F}(V1), P_succ-{F}(V1,V0), P_empty_set-{F}(V2) | pppp17-{T}(V0,V1), pppp17-{T}(V0,V0), pppp17-{T}(V0,V2)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #900: mergings( V0 == V2; #898 ), references = 1, size of lhs = 5:
% 16.41/16.65 P_empty_set-{F}(V0), ordinal-{F}(V1), in-{F}(V1,V2), P_succ-{F}(V1,V3), in-{F}(V2,V3) | pppp21-{T}(V2)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #956: mergings( V4 == V5, V5 == V7; #953 ), references = 1, size of lhs = 7:
% 16.41/16.65 ordinal-{F}(V0), pppp17-{F}(V0,V1), pppp17-{F}(V2,V1), ordinal-{F}(V3), P_succ-{F}(V3,V0), in-{F}(V3,V1), P_empty_set-{F}(V4) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1022: mergings( V2 == V3; #1020 ), references = 2, size of lhs = 5:
% 16.41/16.65 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), pppp17-{F}(V2,V3), in-{F}(V4,V3) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1046: exists( #127, #1044 ), references = 1, size of lhs = 6:
% 16.41/16.65 ordinal-{F}(V0), pppp17-{F}(V0,V1), pppp17-{F}(V2,V1), P_empty_set-{F}(V3), in-{F}(V0,V4), pppp17-{F}(V4,V1) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1118: mergings( V2 == V3; #1116 ), references = 1, size of lhs = 5:
% 16.41/16.65 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), pppp17-{F}(V2,V3), V3 == V0 | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1121: mergings( V2 == V3; #1119 ), references = 1, size of lhs = 4:
% 16.41/16.65 pppp21-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2), P_powerset-{F}(V2,V0) | pppp17-{T}(V0,V1)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1166: mergings( V2 == V3, V3 == V8, V8 == V9; #1162 ), references = 2, size of lhs = 9:
% 16.41/16.65 ordinal-{F}(V0), P_succ-{F}(V0,V1), ordinal-{F}(V1), in-{F}(V0,V2), V1 == V2, pppp17-{F}(V3,V2), P_powerset-{F}(V1,V4), pppp17-{F}(V4,V2), P_empty_set-{F}(V5) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1312: mergings( V5 == V9, V4 == V6, V6 == V7, V7 == V12; #1307 ), references = 1, size of lhs = 12:
% 16.41/16.65 ordinal-{F}(V0), pppp17-{F}(V0,V1), pppp17-{F}(V2,V1), ordinal-{F}(V3), P_succ-{F}(V3,V4), V4 == V1, P_succ-{F}(V4,V0), ordinal-{F}(V4), pppp17-{F}(V5,V1), P_powerset-{F}(V4,V6), pppp17-{F}(V6,V1), P_empty_set-{F}(V7) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1318: mergings( V3 == V7, V2 == V4, V4 == V5, V5 == V8; #1313 ), references = 1, size of lhs = 8:
% 16.41/16.65 pppp21-{F}(V0), ordinal-{F}(V0), ordinal-{F}(V1), P_succ-{F}(V1,V2), P_succ-{F}(V2,V0), ordinal-{F}(V2), P_powerset-{F}(V2,V0), P_empty_set-{F}(V3) | pppp17-{T}(V0,V2)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1544: mergings( V2 == V5, V5 == V6; #1541 ), references = 1, size of lhs = 5:
% 16.41/16.65 pppp19-{F}(V0), ordinal-{F}(V0), P_empty_set-{F}(V1), pppp17-{F}(V0,V2), pppp17-{F}(V3,V2) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1548: mergings( V2 == V3, V3 == V4; #1545 ), references = 2, size of lhs = 4:
% 16.41/16.65 pppp21-{F}(V0), pppp19-{F}(V0), ordinal-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1553: mergings( V0 == V2, V2 == V3, V3 == V4; #1549 ), references = 2, size of lhs = 3:
% 16.41/16.65 pppp19-{F}(V0), ordinal-{F}(V0), P_empty_set-{F}(V1) | pppp1-{T}(V0)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1621: mergings( V2 == V3, V3 == V4; #1616 ), references = 1, size of lhs = 5:
% 16.41/16.65 P_empty_set-{F}(V0), in-{F}(V1,V2), V1 == V0, in-{F}(V2,V3), subset-{F}(V3,V1) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1660: mergings( V2 == V3, V3 == V6, V6 == V7, V7 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V14; #1649 ), references = 1, size of lhs = 13:
% 16.41/16.65 empty-{F}(V0), P_powerset-{F}(V0,V1), epsilon_transitive-{F}(V2), P_powerset-{F}(V2,V1), ordinal-{F}(V2), ordinal-{F}(V3), V2 == V3, P_succ-{F}(V2,V4), ordinal-{F}(V4), P_empty_set-{F}(V5), V3 == V5, in-{F}(V3,V6), in-{F}(V6,V4) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1670: mergings( V2 == V3, V3 == V6, V6 == V7, V7 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15; #1650 ), references = 1, size of lhs = 13:
% 16.41/16.65 empty-{F}(V0), P_powerset-{F}(V0,V1), epsilon_transitive-{F}(V2), P_powerset-{F}(V2,V1), ordinal-{F}(V2), ordinal-{F}(V3), V2 == V3, P_succ-{F}(V2,V4), ordinal-{F}(V4), P_empty_set-{F}(V5), V3 == V5, in-{F}(V3,V6), in-{F}(V6,V4) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1681: mergings( V2 == V3, V3 == V6, V6 == V7, V7 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16; #1651 ), references = 1, size of lhs = 13:
% 16.41/16.65 empty-{F}(V0), P_powerset-{F}(V0,V1), epsilon_transitive-{F}(V2), P_powerset-{F}(V2,V1), ordinal-{F}(V2), ordinal-{F}(V3), V2 == V3, P_succ-{F}(V2,V4), ordinal-{F}(V4), P_empty_set-{F}(V5), V3 == V5, in-{F}(V3,V6), in-{F}(V6,V4) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1693: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V9, V9 == V10, V10 == V11, V11 == V12; #1682 ), references = 1, size of lhs = 11:
% 16.41/16.65 empty-{F}(V0), epsilon_transitive-{F}(V0), ordinal-{F}(V0), ordinal-{F}(V1), V0 == V1, P_succ-{F}(V0,V2), ordinal-{F}(V2), P_empty_set-{F}(V3), V1 == V3, in-{F}(V1,V4), in-{F}(V4,V2) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1703: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13; #1683 ), references = 1, size of lhs = 11:
% 16.41/16.65 empty-{F}(V0), epsilon_transitive-{F}(V0), ordinal-{F}(V0), ordinal-{F}(V1), V0 == V1, P_succ-{F}(V0,V2), ordinal-{F}(V2), P_empty_set-{F}(V3), V1 == V3, in-{F}(V1,V4), in-{F}(V4,V2) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1714: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14; #1684 ), references = 1, size of lhs = 11:
% 16.41/16.65 empty-{F}(V0), epsilon_transitive-{F}(V0), ordinal-{F}(V0), ordinal-{F}(V1), V0 == V1, P_succ-{F}(V0,V2), ordinal-{F}(V2), P_empty_set-{F}(V3), V1 == V3, in-{F}(V1,V4), in-{F}(V4,V2) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1789: exists( #109, #740 ), references = 1, size of lhs = 8:
% 16.41/16.65 pppp21-{F}(V0), ordinal-{F}(V0), epsilon_transitive-{F}(V0), empty-{F}(V1), epsilon_transitive-{F}(V1), ordinal-{F}(V1), P_succ-{F}(V1,V0), P_empty_set-{F}(V2) | pppp17-{T}(V0,V1), pppp17-{T}(V0,V0), pppp17-{T}(V0,V2)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1866: exists( #127, #119 ), references = 3, size of lhs = 1:
% 16.41/16.65 pppp18-{F}(V0,V1) | P_succ-{T}(V1,V0)
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1887: mergings( V2 == V3; #1883 ), references = 2, size of lhs = 4:
% 16.41/16.65 pppp19-{F}(V0), being_limit_ordinal-{F}(V0), pppp1-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1890: mergings( V2 == V3, V3 == V4; #1884 ), references = 1, size of lhs = 4:
% 16.41/16.65 being_limit_ordinal-{F}(V0), pppp19-{F}(V0), ordinal-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1913: mergings( V0 == V2, V2 == V3, V3 == V4; #1908 ), references = 1, size of lhs = 1:
% 16.41/16.65 P_empty_set-{F}(V0) | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 #1916: exists( #129, #1908 ), references = 1, size of lhs = 0:
% 16.41/16.65 FALSE | FALSE
% 16.41/16.65 (used 0 times, uses = {})
% 16.41/16.65
% 16.41/16.65 number of learnt formulas = 61
% 16.41/16.65
% 16.41/16.65
% 16.41/16.65 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.41/16.65
% 16.41/16.65 randbase = 1
%------------------------------------------------------------------------------