TSTP Solution File: SEU238+3 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SEU238+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n017.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 7.00s 7.17s
% Output : Refutation 7.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU238+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jul 22 18:14:29 EDT 2022
% 0.11/0.33 % CPUTime :
% 7.00/7.17 GeoParameters:
% 7.00/7.17
% 7.00/7.17 tptp_input = 1
% 7.00/7.17 tptp_output = 0
% 7.00/7.17 nonempty = 1
% 7.00/7.17 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.00/7.17 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 7.00/7.17
% 7.00/7.17
% 7.00/7.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.00/7.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.00/7.17
% 7.00/7.17 RuleSystem INPUT:
% 7.00/7.17
% 7.00/7.17 Initial Rules:
% 7.00/7.17 #0: input, references = 11, size of lhs = 2:
% 7.00/7.17 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #1: input, references = 5, size of lhs = 2:
% 7.00/7.17 proper_subset-{F}(V0,V1), proper_subset-{F}(V1,V0) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #2: input, references = 3, size of lhs = 1:
% 7.00/7.17 empty-{F}(V0) | function-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #3: input, references = 3, size of lhs = 1:
% 7.00/7.17 ordinal-{F}(V0) | epsilon_transitive-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #4: input, references = 3, size of lhs = 1:
% 7.00/7.17 ordinal-{F}(V0) | epsilon_connected-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #5: input, references = 3, size of lhs = 1:
% 7.00/7.17 empty-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #6: input, references = 3, size of lhs = 3:
% 7.00/7.17 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #7: input, references = 3, size of lhs = 2:
% 7.00/7.17 epsilon_transitive-{F}(V0), epsilon_connected-{F}(V0) | ordinal-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #8: input, references = 3, size of lhs = 1:
% 7.00/7.17 empty-{F}(V0) | epsilon_transitive-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #9: input, references = 3, size of lhs = 1:
% 7.00/7.17 empty-{F}(V0) | epsilon_connected-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #10: input, references = 3, size of lhs = 1:
% 7.00/7.17 empty-{F}(V0) | ordinal-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #11: input, references = 5, size of lhs = 3:
% 7.00/7.17 P_set_union2-{F}(V0,V1,V2), P_set_union2-{F}(V1,V0,V3), V2 == V3 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #12: input, references = 6, size of lhs = 2:
% 7.00/7.17 ordinal-{F}(V0), ordinal-{F}(V1) | ordinal_subset-{T}(V1,V0), ordinal_subset-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #13: input, references = 4, size of lhs = 4:
% 7.00/7.17 P_succ-{F}(V0,V1), P_singleton-{F}(V0,V2), P_set_union2-{F}(V0,V2,V3), V1 == V3 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #14: input, references = 3, size of lhs = 1:
% 7.00/7.17 proper_subset-{F}(V0,V1) | pppp0-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #15: input, references = 10, size of lhs = 1:
% 7.00/7.17 pppp0-{F}(V0,V1) | proper_subset-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #16: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp0-{F}(V0,V1) | subset-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #17: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp0-{F}(V1,V1) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #18: input, references = 10, size of lhs = 2:
% 7.00/7.17 subset-{F}(V0,V1), V0 == V1 | pppp0-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #19: input, references = 4, size of lhs = 1:
% 7.00/7.17 #-{F} V0 | EXISTS V1: pppp2-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #20: input, references = 4, size of lhs = 1:
% 7.00/7.17 pppp2-{F}(V0,V1) | element-{T}(V1,V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #21: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | empty-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #22: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #23: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #24: input, references = 4, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), empty-{F}(V2) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #25: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | empty-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #26: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | pppp3-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #27: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp3-{F}(V0) | ordinal-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #28: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp3-{F}(V0) | epsilon_connected-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #29: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp3-{F}(V0) | epsilon_transitive-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #30: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp3-{F}(V0) | empty-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #31: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp3-{F}(V0) | one_to_one-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #32: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp3-{F}(V0) | function-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #33: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp3-{F}(V0) | relation_empty_yielding-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #34: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp3-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #35: input, references = 3, size of lhs = 4:
% 7.00/7.17 P_empty_set-{F}(V0), relation-{F}(V1), P_set_union2-{F}(V2,V1,V3), relation-{F}(V2) | relation-{T}(V3)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #36: input, references = 3, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), P_set_union2-{F}(V1,V2,V3), empty-{F}(V3) | empty-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #37: input, references = 3, size of lhs = 4:
% 7.00/7.17 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), ordinal-{F}(V1), empty-{F}(V2) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #38: input, references = 4, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), ordinal-{F}(V1) | epsilon_transitive-{T}(V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #39: input, references = 3, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), ordinal-{F}(V1) | epsilon_connected-{T}(V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #40: input, references = 5, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), ordinal-{F}(V1) | ordinal-{T}(V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #41: input, references = 3, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), P_set_union2-{F}(V2,V1,V3), empty-{F}(V3) | empty-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #42: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | empty-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #43: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #44: input, references = 4, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), P_set_union2-{F}(V1,V1,V2), V2 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #45: input, references = 3, size of lhs = 2:
% 7.00/7.17 P_empty_set-{F}(V0), proper_subset-{F}(V1,V1) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #46: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp4-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #47: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp4-{F}(V0) | function-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #48: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp4-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #49: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp5-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #50: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp5-{F}(V0) | ordinal-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #51: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp5-{F}(V0) | epsilon_connected-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #52: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp5-{F}(V0) | epsilon_transitive-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #53: input, references = 4, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp6-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #54: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp6-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #55: input, references = 5, size of lhs = 1:
% 7.00/7.17 pppp6-{F}(V0) | empty-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #56: input, references = 4, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp7-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #57: input, references = 4, size of lhs = 1:
% 7.00/7.17 pppp7-{F}(V0) | empty-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #58: input, references = 4, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp8-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #59: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp8-{F}(V0) | function-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #60: input, references = 5, size of lhs = 1:
% 7.00/7.17 pppp8-{F}(V0) | empty-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #61: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp8-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #62: input, references = 4, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp10-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #63: input, references = 4, size of lhs = 1:
% 7.00/7.17 pppp10-{F}(V0) | pppp9-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #64: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp9-{F}(V0) | ordinal-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #65: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp9-{F}(V0) | epsilon_connected-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #66: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp9-{F}(V0) | epsilon_transitive-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #67: input, references = 4, size of lhs = 1:
% 7.00/7.17 pppp9-{F}(V0) | empty-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #68: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp9-{F}(V0) | one_to_one-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #69: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp9-{F}(V0) | function-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #70: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp9-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #71: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp11-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #72: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp11-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #73: input, references = 3, size of lhs = 2:
% 7.00/7.17 pppp11-{F}(V0), empty-{F}(V0) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #74: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp12-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #75: input, references = 3, size of lhs = 2:
% 7.00/7.17 pppp12-{F}(V0), empty-{F}(V0) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #76: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp13-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #77: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp13-{F}(V0) | one_to_one-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #78: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp13-{F}(V0) | function-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #79: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp13-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #80: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp14-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #81: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp14-{F}(V0) | ordinal-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #82: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp14-{F}(V0) | epsilon_connected-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #83: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp14-{F}(V0) | epsilon_transitive-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #84: input, references = 3, size of lhs = 2:
% 7.00/7.17 pppp14-{F}(V0), empty-{F}(V0) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #85: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp15-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #86: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp15-{F}(V0) | relation_empty_yielding-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #87: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp15-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #88: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp16-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #89: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp16-{F}(V0) | function-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #90: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp16-{F}(V0) | relation_empty_yielding-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #91: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp16-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #92: input, references = 3, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp17-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #93: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp17-{F}(V0) | function-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #94: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp17-{F}(V0) | relation_non_empty-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #95: input, references = 3, size of lhs = 1:
% 7.00/7.17 pppp17-{F}(V0) | relation-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #96: input, references = 10, size of lhs = 4:
% 7.00/7.17 P_empty_set-{F}(V0), ordinal-{F}(V1), ordinal-{F}(V2), ordinal_subset-{F}(V2,V1) | subset-{T}(V2,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #97: input, references = 3, size of lhs = 4:
% 7.00/7.17 P_empty_set-{F}(V0), ordinal-{F}(V1), ordinal-{F}(V2), subset-{F}(V2,V1) | ordinal_subset-{T}(V2,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #98: input, references = 3, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), ordinal-{F}(V1), ordinal-{F}(V2) | ordinal_subset-{T}(V2,V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #99: input, references = 3, size of lhs = 2:
% 7.00/7.17 P_empty_set-{F}(V0), #-{F} V1 | subset-{T}(V1,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #100: input, references = 4, size of lhs = 2:
% 7.00/7.17 P_empty_set-{F}(V0), P_succ-{F}(V1,V2) | in-{T}(V1,V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #101: input, references = 4, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), P_set_union2-{F}(V1,V0,V2), V2 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #102: input, references = 4, size of lhs = 2:
% 7.00/7.17 P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #103: input, references = 7, size of lhs = 4:
% 7.00/7.17 P_empty_set-{F}(V0), epsilon_transitive-{F}(V1), ordinal-{F}(V2), proper_subset-{F}(V1,V2) | in-{T}(V1,V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #104: input, references = 4, size of lhs = 2:
% 7.00/7.17 P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #105: input, references = 8, size of lhs = 5:
% 7.00/7.17 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)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #106: input, references = 7, size of lhs = 5:
% 7.00/7.17 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)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #107: input, references = 3, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3) | subset-{T}(V1,V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #108: input, references = 3, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), subset-{F}(V1,V2) | element-{T}(V1,V3)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #109: input, references = 4, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), ordinal-{F}(V1), being_limit_ordinal-{F}(V1) | pppp1-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #110: input, references = 5, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), ordinal-{F}(V1), pppp1-{F}(V1) | being_limit_ordinal-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #111: input, references = 6, size of lhs = 5:
% 7.00/7.17 P_empty_set-{F}(V0), pppp1-{F}(V1), P_succ-{F}(V2,V3), ordinal-{F}(V2), in-{F}(V2,V1) | in-{T}(V3,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #112: input, references = 8, size of lhs = 2:
% 7.00/7.17 P_empty_set-{F}(V0), #-{F} V1 | pppp1-{T}(V1), pppp22-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #113: input, references = 6, size of lhs = 1:
% 7.00/7.17 pppp22-{F}(V0) | EXISTS V1: pppp18-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #114: input, references = 4, size of lhs = 3:
% 7.00/7.17 pppp18-{F}(V0,V1), P_succ-{F}(V1,V2), in-{F}(V2,V0) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #115: input, references = 10, size of lhs = 2:
% 7.00/7.17 pppp18-{F}(V0,V1), P_succ-{F}(V1,V2) | in-{T}(V1,V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #116: input, references = 5, size of lhs = 2:
% 7.00/7.17 pppp18-{F}(V0,V1), P_succ-{F}(V1,V2) | ordinal-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #117: input, references = 4, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | EXISTS V1: pppp21-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #118: input, references = 4, size of lhs = 1:
% 7.00/7.17 pppp21-{F}(V0) | pppp20-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #119: input, references = 4, size of lhs = 3:
% 7.00/7.17 pppp20-{F}(V2), P_succ-{F}(V1,V2), ordinal-{F}(V1) | being_limit_ordinal-{T}(V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #120: input, references = 3, size of lhs = 3:
% 7.00/7.17 pppp20-{F}(V2), P_succ-{F}(V1,V2), ordinal-{F}(V1) | EXISTS V3: pppp19-{T}(V2,V3)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #121: input, references = 5, size of lhs = 2:
% 7.00/7.17 pppp20-{F}(V0), being_limit_ordinal-{F}(V0) | EXISTS V1: pppp19-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #122: input, references = 4, size of lhs = 1:
% 7.00/7.17 pppp20-{F}(V0) | ordinal-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #123: input, references = 4, size of lhs = 3:
% 7.00/7.17 pppp19-{F}(V0,V1), P_succ-{F}(V1,V2), V0 == V2 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #124: input, references = 4, size of lhs = 2:
% 7.00/7.17 pppp19-{F}(V0,V1), P_succ-{F}(V1,V2) | ordinal-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #125: input, references = 3, size of lhs = 4:
% 7.00/7.17 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3), in-{F}(V4,V1) | element-{T}(V4,V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #126: input, references = 5, size of lhs = 5:
% 7.00/7.17 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V1), element-{F}(V3,V2), in-{F}(V4,V3) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #127: input, references = 7, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #128: input, references = 6, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #129: input, references = 5, size of lhs = 4:
% 7.00/7.17 P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #130: input, references = 6, size of lhs = 2:
% 7.00/7.17 #-{F} V0, #-{F} V1 | EXISTS V2: P_set_union2-{T}(V0,V1,V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #131: input, references = 11, size of lhs = 1:
% 7.00/7.17 #-{F} V0 | EXISTS V1: P_succ-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #132: input, references = 4, size of lhs = 1:
% 7.00/7.17 #-{F} V0 | EXISTS V1: P_singleton-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #133: input, references = 4, size of lhs = 0:
% 7.00/7.17 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #134: input, references = 3, size of lhs = 1:
% 7.00/7.17 #-{F} V0 | EXISTS V1: P_powerset-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 number of initial rules = 135
% 7.00/7.17
% 7.00/7.17 Simplifiers:
% 7.00/7.17 #135: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 relation_non_empty-{F}(V0), relation_non_empty-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #136: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 P_set_union2-{F}(V0,V1,V2), P_set_union2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #137: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 P_succ-{F}(V0,V1), P_succ-{F}(V0,V3), V1 == V3 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #138: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 P_singleton-{F}(V0,V1), P_singleton-{F}(V0,V3), V1 == V3 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #139: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #140: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 P_powerset-{F}(V0,V1), P_powerset-{F}(V0,V3), V1 == V3 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #141: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp2-{F}(V0,V1), pppp2-{F}(V0,V3), V1 == V3 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #142: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp3-{F}(V0), pppp3-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #143: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp4-{F}(V0), pppp4-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #144: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #145: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #146: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp7-{F}(V0), pppp7-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #147: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #148: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #149: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp10-{F}(V0), pppp10-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #150: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp11-{F}(V0), pppp11-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #151: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp12-{F}(V0), pppp12-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #152: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp13-{F}(V0), pppp13-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #153: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp14-{F}(V0), pppp14-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #154: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp15-{F}(V0), pppp15-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #155: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp16-{F}(V0), pppp16-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #156: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp17-{F}(V0), pppp17-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #157: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp18-{F}(V0,V1), pppp18-{F}(V0,V3), V1 == V3 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #158: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp19-{F}(V0,V1), pppp19-{F}(V0,V3), V1 == V3 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #159: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp19-{F}(V0,V1), pppp19-{F}(V2,V3), V0 == V2 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #160: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp20-{F}(V0), pppp20-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #161: unsound, references = 3, size of lhs = 3:
% 7.00/7.17 pppp21-{F}(V0), pppp21-{F}(V1), V0 == V1 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 number of simplifiers = 27
% 7.00/7.17
% 7.00/7.17 Learnt:
% 7.00/7.17 #164: exists( #130, #44 ), references = 1, size of lhs = 2:
% 7.00/7.17 P_empty_set-{F}(V0), #-{F} V1 | P_set_union2-{T}(V1,V1,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #170: mergings( V0 == V2; #168 ), references = 1, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | pppp7-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #176: mergings( V0 == V2; #173 ), references = 1, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | pppp6-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #178: mergings( V0 == V2; #174 ), references = 1, size of lhs = 2:
% 7.00/7.17 P_empty_set-{F}(V0), empty-{F}(V1) | pppp6-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #185: mergings( V0 == V2; #182 ), references = 1, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | pppp8-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #187: mergings( V0 == V2; #183 ), references = 1, size of lhs = 2:
% 7.00/7.17 P_empty_set-{F}(V0), empty-{F}(V1) | pppp8-{T}(V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #196: mergings( V0 == V2; #194 ), references = 1, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | pppp10-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #212: exists( #130, #101 ), references = 2, size of lhs = 2:
% 7.00/7.17 P_empty_set-{F}(V0), #-{F} V1 | P_set_union2-{T}(V1,V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #236: exists( #130, #11 ), references = 1, size of lhs = 1:
% 7.00/7.17 P_set_union2-{F}(V0,V1,V2) | P_set_union2-{T}(V1,V0,V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #237: exists( #130, #13 ), references = 2, size of lhs = 2:
% 7.00/7.17 P_succ-{F}(V0,V1), P_singleton-{F}(V0,V2) | P_set_union2-{T}(V0,V2,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #247: mergings( V0 == V3; #243 ), references = 2, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), element-{F}(V1,V2), V2 == V0 | in-{T}(V1,V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #250: mergings( V0 == V3, V2 == V3; #244 ), references = 1, size of lhs = 4:
% 7.00/7.17 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, element-{F}(V2,V0) | in-{T}(V2,V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #252: mergings( V2 == V0; #245 ), references = 1, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), pppp11-{F}(V0), element-{F}(V1,V0) | in-{T}(V1,V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #274: exists( #132, #270 ), references = 1, size of lhs = 2:
% 7.00/7.17 P_empty_set-{F}(V0), P_succ-{F}(V0,V1) | P_singleton-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #288: mergings( V2 == V4; #284 ), references = 2, size of lhs = 6:
% 7.00/7.17 ordinal-{F}(V0), ordinal-{F}(V1), P_succ-{F}(V1,V0), ordinal-{F}(V2), empty-{F}(V2), P_empty_set-{F}(V3) | ordinal_subset-{T}(V2,V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #289: disj( #12, #106+#0 ), references = 1, size of lhs = 6:
% 7.00/7.17 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)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #303: mergings( V0 == V2; #301 ), references = 1, size of lhs = 4:
% 7.00/7.17 P_empty_set-{F}(V0), ordinal-{F}(V1), P_succ-{F}(V1,V2), in-{F}(V1,V2) | pppp22-{T}(V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #334: mergings( V2 == V6; #332 ), references = 1, size of lhs = 8:
% 7.00/7.17 ordinal-{F}(V0), P_succ-{F}(V0,V1), ordinal-{F}(V1), in-{F}(V0,V2), V1 == V2, proper_subset-{F}(V2,V1), pppp18-{F}(V3,V2), P_empty_set-{F}(V4) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #343: mergings( V0 == V2; #341 ), references = 1, size of lhs = 5:
% 7.00/7.17 P_empty_set-{F}(V0), ordinal-{F}(V1), in-{F}(V1,V2), P_succ-{F}(V1,V3), in-{F}(V2,V3) | pppp22-{T}(V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #360: exists( #131, #123 ), references = 2, size of lhs = 1:
% 7.00/7.17 pppp19-{F}(V0,V1) | P_succ-{T}(V1,V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #364: exists( #121, #361 ), references = 1, size of lhs = 4:
% 7.00/7.17 pppp20-{F}(V0), being_limit_ordinal-{F}(V0), empty-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #369: mergings( V0 == V2, V2 == V3; #366 ), references = 1, size of lhs = 4:
% 7.00/7.17 ordinal-{F}(V0), pppp20-{F}(V0), empty-{F}(V0), P_empty_set-{F}(V1) | pppp22-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #393: disj( #12, #106+#0 ), references = 1, size of lhs = 4:
% 7.00/7.17 ordinal-{F}(V0), P_empty_set-{F}(V1), ordinal-{F}(V2), P_succ-{F}(V2,V0) | ordinal_subset-{T}(V2,V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #432: exists( #131, #426 ), references = 1, size of lhs = 3:
% 7.00/7.17 P_empty_set-{F}(V0), empty-{F}(V1), pppp18-{F}(V1,V2) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #433: exists( #131, #428 ), references = 1, size of lhs = 5:
% 7.00/7.17 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V3,V2), pppp18-{F}(V3,V4) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #434: exists( #131, #427 ), references = 2, size of lhs = 2:
% 7.00/7.17 pppp18-{F}(V0,V1), in-{F}(V0,V1) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #438: exists( #113, #429 ), references = 1, size of lhs = 3:
% 7.00/7.17 pppp22-{F}(V0), empty-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #439: exists( #113, #431 ), references = 1, size of lhs = 5:
% 7.00/7.17 pppp22-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2), P_powerset-{F}(V2,V3), element-{F}(V0,V3) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #443: mergings( V0 == V2; #440 ), references = 1, size of lhs = 2:
% 7.00/7.17 empty-{F}(V0), P_empty_set-{F}(V1) | pppp1-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #445: mergings( V0 == V2; #441 ), references = 1, size of lhs = 4:
% 7.00/7.17 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V3,V2) | pppp1-{T}(V3)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #506: mergings( V2 == V3, V3 == V4, V4 == V6; #502 ), references = 2, size of lhs = 7:
% 7.00/7.17 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)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #532: mergings( V2 == V4, V4 == V5, V5 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11; #524 ), references = 1, size of lhs = 8:
% 7.00/7.17 empty-{F}(V0), epsilon_transitive-{F}(V0), ordinal-{F}(V0), ordinal-{F}(V1), in-{F}(V1,V2), ordinal-{F}(V2), P_succ-{F}(V0,V2), P_empty_set-{F}(V3) | P_succ-{T}(V1,V0), P_succ-{T}(V1,V2)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #550: mergings( V0 == V2, V2 == V3, V3 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V12, V12 == V13, V13 == V14, V14 == V15; #538 ), references = 1, size of lhs = 14:
% 7.00/7.17 empty-{F}(V0), epsilon_transitive-{F}(V0), ordinal-{F}(V0), ordinal-{F}(V1), P_succ-{F}(V0,V1), epsilon_transitive-{F}(V2), ordinal-{F}(V2), empty-{F}(V2), P_succ-{F}(V2,V1), ordinal-{F}(V3), V3 == V2, in-{F}(V3,V1), epsilon_transitive-{F}(V3), P_empty_set-{F}(V4) | P_succ-{T}(V3,V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #575: exists( #131, #570 ), references = 1, size of lhs = 1:
% 7.00/7.17 pppp18-{F}(V0,V0) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #576: exists( #131, #571 ), references = 1, size of lhs = 2:
% 7.00/7.17 pppp18-{F}(V0,V1), pppp18-{F}(V1,V0) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #649: mergings( V2 == V3; #647 ), references = 2, size of lhs = 5:
% 7.00/7.17 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), pppp18-{F}(V2,V3), in-{F}(V4,V3) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #680: mergings( V2 == V3; #678 ), references = 1, size of lhs = 5:
% 7.00/7.17 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), pppp18-{F}(V2,V3), V3 == V0 | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #683: mergings( V2 == V3; #681 ), references = 1, size of lhs = 4:
% 7.00/7.17 pppp22-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2), P_powerset-{F}(V2,V0) | pppp18-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #733: mergings( V2 == V3; #730 ), references = 2, size of lhs = 4:
% 7.00/7.17 pppp20-{F}(V0), being_limit_ordinal-{F}(V0), pppp1-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #739: mergings( V0 == V2, V2 == V3, V3 == V4; #735 ), references = 2, size of lhs = 3:
% 7.00/7.17 ordinal-{F}(V0), pppp20-{F}(V0), P_empty_set-{F}(V1) | pppp22-{T}(V0)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #794: mergings( V2 == V3, V3 == V4, V4 == V6, V6 == V7; #789 ), references = 2, size of lhs = 5:
% 7.00/7.17 ordinal-{F}(V0), in-{F}(V0,V1), ordinal-{F}(V1), pppp18-{F}(V1,V0), P_empty_set-{F}(V2) | P_succ-{T}(V0,V1)
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #829: mergings( V2 == V5, V5 == V6; #826 ), references = 1, size of lhs = 5:
% 7.00/7.17 ordinal-{F}(V0), pppp20-{F}(V0), pppp18-{F}(V0,V1), pppp18-{F}(V2,V1), P_empty_set-{F}(V3) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #833: mergings( V2 == V3, V3 == V4; #830 ), references = 2, size of lhs = 4:
% 7.00/7.17 pppp22-{F}(V0), ordinal-{F}(V0), pppp20-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #842: mergings( V0 == V2, V2 == V3; #839 ), references = 1, size of lhs = 1:
% 7.00/7.17 P_empty_set-{F}(V0) | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 #844: exists( #133, #839 ), references = 1, size of lhs = 0:
% 7.00/7.17 FALSE | FALSE
% 7.00/7.17 (used 0 times, uses = {})
% 7.00/7.17
% 7.00/7.17 number of learnt formulas = 45
% 7.00/7.17
% 7.00/7.17
% 7.00/7.17 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.00/7.17
% 7.00/7.17 randbase = 1
%------------------------------------------------------------------------------