TSTP Solution File: SEU296+3 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SEU296+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n008.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 06:17:44 EDT 2022
% Result : Theorem 11.11s 11.32s
% Output : Refutation 11.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU296+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jul 22 19:12:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 11.11/11.32 GeoParameters:
% 11.11/11.32
% 11.11/11.32 tptp_input = 1
% 11.11/11.32 tptp_output = 0
% 11.11/11.32 nonempty = 1
% 11.11/11.32 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.11/11.32 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 11.11/11.32
% 11.11/11.32
% 11.11/11.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.11/11.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.11/11.32
% 11.11/11.32 RuleSystem INPUT:
% 11.11/11.32
% 11.11/11.32 Initial Rules:
% 11.11/11.32 #0: input, references = 3, size of lhs = 2:
% 11.11/11.32 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #1: input, references = 3, size of lhs = 2:
% 11.11/11.32 ordinal-{F}(V0), element-{F}(V1,V0) | epsilon_transitive-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #2: input, references = 3, size of lhs = 2:
% 11.11/11.32 ordinal-{F}(V0), element-{F}(V1,V0) | epsilon_connected-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #3: input, references = 3, size of lhs = 2:
% 11.11/11.32 ordinal-{F}(V0), element-{F}(V1,V0) | ordinal-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #4: input, references = 3, size of lhs = 1:
% 11.11/11.32 empty-{F}(V0) | finite-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #5: input, references = 3, size of lhs = 1:
% 11.11/11.32 empty-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #6: input, references = 3, size of lhs = 1:
% 11.11/11.32 ordinal-{F}(V0) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #7: input, references = 3, size of lhs = 1:
% 11.11/11.32 ordinal-{F}(V0) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #8: input, references = 3, size of lhs = 1:
% 11.11/11.32 empty-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #9: input, references = 3, size of lhs = 2:
% 11.11/11.32 empty-{F}(V0), ordinal-{F}(V0) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #10: input, references = 3, size of lhs = 2:
% 11.11/11.32 empty-{F}(V0), ordinal-{F}(V0) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #11: input, references = 3, size of lhs = 2:
% 11.11/11.32 empty-{F}(V0), ordinal-{F}(V0) | natural-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #12: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_powerset-{F}(V0,V1), finite-{F}(V0), element-{F}(V2,V1) | finite-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #13: input, references = 3, size of lhs = 3:
% 11.11/11.32 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #14: input, references = 3, size of lhs = 2:
% 11.11/11.32 epsilon_transitive-{F}(V0), epsilon_connected-{F}(V0) | ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #15: input, references = 3, size of lhs = 2:
% 11.11/11.32 P_omega-{F}(V0), element-{F}(V1,V0) | epsilon_transitive-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #16: input, references = 3, size of lhs = 2:
% 11.11/11.32 P_omega-{F}(V0), element-{F}(V1,V0) | epsilon_connected-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #17: input, references = 3, size of lhs = 2:
% 11.11/11.32 P_omega-{F}(V0), element-{F}(V1,V0) | ordinal-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #18: input, references = 3, size of lhs = 2:
% 11.11/11.32 P_omega-{F}(V0), element-{F}(V1,V0) | natural-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #19: input, references = 3, size of lhs = 2:
% 11.11/11.32 P_omega-{F}(V0), empty-{F}(V1) | epsilon_transitive-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #20: input, references = 3, size of lhs = 2:
% 11.11/11.32 P_omega-{F}(V0), empty-{F}(V1) | epsilon_connected-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #21: input, references = 3, size of lhs = 2:
% 11.11/11.32 P_omega-{F}(V0), empty-{F}(V1) | ordinal-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #22: input, references = 3, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), element-{F}(V2,V1), ordinal-{F}(V2) | epsilon_transitive-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #23: input, references = 3, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), element-{F}(V2,V1), ordinal-{F}(V2) | epsilon_connected-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #24: input, references = 3, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), element-{F}(V2,V1), ordinal-{F}(V2) | natural-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #25: input, references = 4, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_set_intersection2-{F}(V2,V3,V4), P_set_intersection2-{F}(V3,V2,V5), V4 == V5 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #26: input, references = 5, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), finite-{F}(V2) | pppp0-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #27: input, references = 4, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), pppp0-{F}(V2) | finite-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #28: input, references = 6, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), pppp0-{F}(V2) | EXISTS V3: pppp1-{T}(V2,V3,V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #29: input, references = 4, size of lhs = 7:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_relation_rng-{F}(V3,V2), P_relation_dom-{F}(V3,V5), relation-{F}(V3), function-{F}(V3), in-{F}(V5,V0) | pppp0-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #30: input, references = 4, size of lhs = 3:
% 11.11/11.32 pppp1-{F}(V0,V1,V2), P_relation_rng-{F}(V1,V3), P_relation_dom-{F}(V1,V4) | in-{T}(V4,V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #31: input, references = 4, size of lhs = 4:
% 11.11/11.32 pppp1-{F}(V0,V1,V2), P_relation_rng-{F}(V1,V3), P_relation_dom-{F}(V1,V4), V3 == V0 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #32: input, references = 4, size of lhs = 3:
% 11.11/11.32 pppp1-{F}(V0,V1,V2), P_relation_rng-{F}(V1,V3), P_relation_dom-{F}(V1,V4) | function-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #33: input, references = 10, size of lhs = 3:
% 11.11/11.32 pppp1-{F}(V0,V1,V2), P_relation_rng-{F}(V1,V3), P_relation_dom-{F}(V1,V4) | relation-{T}(V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #34: input, references = 5, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), relation-{F}(V2), P_relation_composition-{F}(V3,V2,V4), relation-{F}(V3) | relation-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #35: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), #-{F} V2 | EXISTS V3: pppp2-{T}(V2,V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #36: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp2-{F}(V0,V1) | element-{T}(V1,V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #37: input, references = 4, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), finite-{F}(V2), P_set_intersection2-{F}(V3,V2,V4) | finite-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #38: input, references = 5, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), relation-{F}(V2), P_relation_composition-{F}(V2,V3,V4), empty-{F}(V3) | empty-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #39: input, references = 3, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), relation-{F}(V2), P_relation_composition-{F}(V2,V3,V4), empty-{F}(V3) | relation-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #40: input, references = 3, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), finite-{F}(V2), P_set_intersection2-{F}(V2,V3,V4) | finite-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #41: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | empty-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #42: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | relation-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #43: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | relation_empty_yielding-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #44: input, references = 3, size of lhs = 8:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V4,V3,V5), relation-{F}(V4), function-{F}(V4) | relation-{T}(V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #45: input, references = 4, size of lhs = 8:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V4,V3,V5), relation-{F}(V4), function-{F}(V4) | function-{T}(V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #46: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #47: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #48: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #49: input, references = 3, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V0) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #50: input, references = 3, size of lhs = 6:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), P_set_intersection2-{F}(V4,V3,V5), relation-{F}(V4) | relation-{T}(V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #51: input, references = 4, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V3,V4), empty-{F}(V4) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #52: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | empty-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #53: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | pppp3-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #54: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp3-{F}(V0) | ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #55: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp3-{F}(V0) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #56: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp3-{F}(V0) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #57: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp3-{F}(V0) | empty-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #58: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp3-{F}(V0) | one_to_one-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #59: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp3-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #60: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp3-{F}(V0) | relation_empty_yielding-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #61: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp3-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #62: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | empty-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #63: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | relation-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #64: input, references = 3, size of lhs = 7:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_dom-{F}(V3,V4), relation-{F}(V3), function-{F}(V3), transfinite_sequence-{F}(V3) | epsilon_transitive-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #65: input, references = 3, size of lhs = 7:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_dom-{F}(V3,V4), relation-{F}(V3), function-{F}(V3), transfinite_sequence-{F}(V3) | epsilon_connected-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #66: input, references = 3, size of lhs = 7:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_dom-{F}(V3,V4), relation-{F}(V3), function-{F}(V3), transfinite_sequence-{F}(V3) | ordinal-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #67: input, references = 5, size of lhs = 6:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_dom-{F}(V3,V4), relation-{F}(V3), empty-{F}(V4) | empty-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #68: input, references = 3, size of lhs = 7:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V3,V4), relation-{F}(V3), relation_non_empty-{F}(V3), function-{F}(V3) | with_non_empty_elements-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #69: input, references = 6, size of lhs = 6:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V3,V4), relation-{F}(V3), empty-{F}(V4) | empty-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #70: input, references = 4, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_dom-{F}(V3,V4), empty-{F}(V3) | empty-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #71: input, references = 3, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_dom-{F}(V3,V4), empty-{F}(V3) | relation-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #72: input, references = 3, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V1) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #73: input, references = 3, size of lhs = 9:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), function-{F}(V3), function_yielding-{F}(V3), P_relation_composition-{F}(V4,V3,V5), relation-{F}(V4), function-{F}(V4) | relation-{T}(V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #74: input, references = 3, size of lhs = 9:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), function-{F}(V3), function_yielding-{F}(V3), P_relation_composition-{F}(V4,V3,V5), relation-{F}(V4), function-{F}(V4) | function-{T}(V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #75: input, references = 3, size of lhs = 9:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), function-{F}(V3), function_yielding-{F}(V3), P_relation_composition-{F}(V4,V3,V5), relation-{F}(V4), function-{F}(V4) | function_yielding-{T}(V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #76: input, references = 5, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V3,V4), empty-{F}(V3) | empty-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #77: input, references = 3, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V3,V4), empty-{F}(V3) | relation-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #78: input, references = 4, size of lhs = 6:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), P_relation_composition-{F}(V4,V3,V5), empty-{F}(V4) | empty-{T}(V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #79: input, references = 3, size of lhs = 6:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), P_relation_composition-{F}(V4,V3,V5), empty-{F}(V4) | relation-{T}(V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #80: input, references = 4, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_set_intersection2-{F}(V3,V3,V4), V4 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #81: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp5-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #82: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp5-{F}(V0) | pppp4-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #83: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp4-{F}(V0) | natural-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #84: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp4-{F}(V0) | ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #85: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp4-{F}(V0) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #86: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp4-{F}(V0) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #87: input, references = 3, size of lhs = 2:
% 11.11/11.32 pppp4-{F}(V0), empty-{F}(V0) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #88: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp6-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #89: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp6-{F}(V0) | finite-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #90: input, references = 3, size of lhs = 2:
% 11.11/11.32 pppp6-{F}(V0), empty-{F}(V0) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #91: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp7-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #92: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp7-{F}(V0) | function_yielding-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #93: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp7-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #94: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp7-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #95: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp8-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #96: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp8-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #97: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp8-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #98: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp9-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #99: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp9-{F}(V0) | ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #100: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp9-{F}(V0) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #101: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp9-{F}(V0) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #102: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp10-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #103: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp10-{F}(V0) | being_limit_ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #104: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp10-{F}(V0) | ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #105: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp10-{F}(V0) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #106: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp10-{F}(V0) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #107: input, references = 4, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp11-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #108: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp11-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #109: input, references = 5, size of lhs = 1:
% 11.11/11.32 pppp11-{F}(V0) | empty-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #110: input, references = 4, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V3,V4) | empty-{T}(V3), pppp36-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #111: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp36-{F}(V0) | EXISTS V1: pppp12-{T}(V1,V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #112: input, references = 3, size of lhs = 2:
% 11.11/11.32 pppp12-{F}(V0,V1), empty-{F}(V0) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #113: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp12-{F}(V0,V1) | element-{T}(V0,V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #114: input, references = 4, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp13-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #115: input, references = 5, size of lhs = 1:
% 11.11/11.32 pppp13-{F}(V0) | empty-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #116: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp15-{T}(V1,V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #117: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp15-{F}(V0,V1) | pppp14-{T}(V1,V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #118: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp14-{F}(V0,V1) | ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #119: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp14-{F}(V0,V1) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #120: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp14-{F}(V0,V1) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #121: input, references = 3, size of lhs = 2:
% 11.11/11.32 pppp14-{F}(V0,V1), empty-{F}(V0) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #122: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp14-{F}(V0,V1) | element-{T}(V0,V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #123: input, references = 4, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V3,V4) | EXISTS V5: pppp17-{T}(V4,V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #124: input, references = 4, size of lhs = 1:
% 11.11/11.32 pppp17-{F}(V0,V1) | pppp16-{T}(V1,V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #125: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp16-{F}(V0,V1) | finite-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #126: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp16-{F}(V0,V1) | natural-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #127: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp16-{F}(V0,V1) | ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #128: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp16-{F}(V0,V1) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #129: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp16-{F}(V0,V1) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #130: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp16-{F}(V0,V1) | one_to_one-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #131: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp16-{F}(V0,V1) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #132: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp16-{F}(V0,V1) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #133: input, references = 4, size of lhs = 1:
% 11.11/11.32 pppp16-{F}(V0,V1) | empty-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #134: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp16-{F}(V0,V1) | element-{T}(V0,V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #135: input, references = 4, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp18-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #136: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp18-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #137: input, references = 5, size of lhs = 1:
% 11.11/11.32 pppp18-{F}(V0) | empty-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #138: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp18-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #139: input, references = 4, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp20-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #140: input, references = 5, size of lhs = 1:
% 11.11/11.32 pppp20-{F}(V0) | pppp19-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #141: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp19-{F}(V0) | ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #142: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp19-{F}(V0) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #143: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp19-{F}(V0) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #144: input, references = 5, size of lhs = 1:
% 11.11/11.32 pppp19-{F}(V0) | empty-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #145: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp19-{F}(V0) | one_to_one-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #146: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp19-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #147: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp19-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #148: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp21-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #149: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp21-{F}(V0) | ordinal_yielding-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #150: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp21-{F}(V0) | transfinite_sequence-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #151: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp21-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #152: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp21-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #153: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp22-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #154: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp22-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #155: input, references = 3, size of lhs = 2:
% 11.11/11.32 pppp22-{F}(V0), empty-{F}(V0) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #156: input, references = 4, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V3,V4) | EXISTS V5: pppp23-{T}(V5,V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #157: input, references = 4, size of lhs = 1:
% 11.11/11.32 pppp23-{F}(V0,V1) | empty-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #158: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp23-{F}(V0,V1) | element-{T}(V0,V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #159: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp24-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #160: input, references = 3, size of lhs = 2:
% 11.11/11.32 pppp24-{F}(V0), empty-{F}(V0) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #161: input, references = 4, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp26-{T}(V1,V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #162: input, references = 4, size of lhs = 1:
% 11.11/11.32 pppp26-{F}(V0,V1) | pppp25-{T}(V1,V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #163: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp25-{F}(V0,V1) | natural-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #164: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp25-{F}(V0,V1) | ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #165: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp25-{F}(V0,V1) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #166: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp25-{F}(V0,V1) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #167: input, references = 4, size of lhs = 1:
% 11.11/11.32 pppp25-{F}(V0,V1) | empty-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #168: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp25-{F}(V0,V1) | element-{T}(V0,V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #169: input, references = 4, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V3,V4) | empty-{T}(V3), pppp37-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #170: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp37-{F}(V0) | EXISTS V1: pppp27-{T}(V1,V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #171: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp27-{F}(V0,V1) | finite-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #172: input, references = 3, size of lhs = 2:
% 11.11/11.32 pppp27-{F}(V0,V1), empty-{F}(V0) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #173: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp27-{F}(V0,V1) | element-{T}(V0,V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #174: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp28-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #175: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp28-{F}(V0) | one_to_one-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #176: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp28-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #177: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp28-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #178: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp29-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #179: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp29-{F}(V0) | ordinal-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #180: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp29-{F}(V0) | epsilon_connected-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #181: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp29-{F}(V0) | epsilon_transitive-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #182: input, references = 3, size of lhs = 2:
% 11.11/11.32 pppp29-{F}(V0), empty-{F}(V0) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #183: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp30-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #184: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp30-{F}(V0) | relation_empty_yielding-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #185: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp30-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #186: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp31-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #187: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp31-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #188: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp31-{F}(V0) | relation_empty_yielding-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #189: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp31-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #190: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp32-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #191: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp32-{F}(V0) | transfinite_sequence-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #192: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp32-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #193: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp32-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #194: input, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp33-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #195: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp33-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #196: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp33-{F}(V0) | relation_non_empty-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #197: input, references = 3, size of lhs = 1:
% 11.11/11.32 pppp33-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #198: input, references = 3, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), #-{F} V3 | subset-{T}(V3,V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #199: input, references = 5, size of lhs = 9:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_dom-{F}(V3,V4), relation-{F}(V3), P_relation_image-{F}(V3,V5,V6), P_set_intersection2-{F}(V4,V5,V7), P_relation_image-{F}(V3,V7,V8), V6 == V8 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #200: input, references = 3, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), finite-{F}(V3), P_set_intersection2-{F}(V3,V4,V5) | finite-{T}(V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #201: input, references = 7, size of lhs = 10:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V3,V4), relation-{F}(V3), P_relation_composition-{F}(V3,V5,V6), P_relation_rng-{F}(V6,V7), P_relation_image-{F}(V5,V4,V8), relation-{F}(V5), V7 == V8 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #202: input, references = 4, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | EXISTS V3: pppp35-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #203: input, references = 4, size of lhs = 1:
% 11.11/11.32 pppp35-{F}(V0) | EXISTS V1: pppp34-{T}(V1,V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #204: input, references = 4, size of lhs = 1:
% 11.11/11.32 pppp35-{F}(V0) | function-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #205: input, references = 4, size of lhs = 1:
% 11.11/11.32 pppp35-{F}(V0) | relation-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #206: input, references = 4, size of lhs = 3:
% 11.11/11.32 pppp34-{F}(V0,V1), P_relation_image-{F}(V1,V0,V2), finite-{F}(V2) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #207: input, references = 5, size of lhs = 2:
% 11.11/11.32 pppp34-{F}(V0,V1), P_relation_image-{F}(V1,V0,V2) | finite-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #208: input, references = 4, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_set_intersection2-{F}(V3,V4,V5) | subset-{T}(V5,V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #209: input, references = 3, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), in-{F}(V3,V4) | element-{T}(V3,V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #210: input, references = 4, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_set_intersection2-{F}(V3,V2,V4), V4 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #211: input, references = 7, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), element-{F}(V4,V3) | empty-{T}(V3), in-{T}(V4,V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #212: input, references = 3, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V4,V5), element-{F}(V3,V5) | subset-{T}(V3,V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #213: input, references = 3, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V4,V5), subset-{F}(V3,V4) | element-{T}(V3,V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #214: input, references = 5, size of lhs = 12:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V3,V4), P_relation_dom-{F}(V3,V5), relation-{F}(V3), P_relation_dom-{F}(V6,V7), P_relation_composition-{F}(V3,V6,V8), P_relation_dom-{F}(V8,V9), relation-{F}(V6), subset-{F}(V4,V7), V9 == V5 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #215: input, references = 3, size of lhs = 6:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V4,V5), element-{F}(V3,V5), in-{F}(V6,V3) | element-{T}(V6,V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #216: input, references = 3, size of lhs = 7:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V3,V4), empty-{F}(V3), element-{F}(V5,V4), in-{F}(V6,V5) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #217: input, references = 16, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3), V3 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #218: input, references = 4, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3), in-{F}(V4,V3) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #219: input, references = 10, size of lhs = 6:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3), empty-{F}(V4), V4 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #220: input, references = 3, size of lhs = 1:
% 11.11/11.32 #-{F} V0 | EXISTS V1: P_powerset-{T}(V0,V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #221: input, references = 4, size of lhs = 0:
% 11.11/11.32 FALSE | EXISTS V0: P_omega-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #222: input, references = 4, size of lhs = 0:
% 11.11/11.32 FALSE | EXISTS V0: P_positive_rationals-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #223: input, references = 7, size of lhs = 2:
% 11.11/11.32 #-{F} V0, #-{F} V1 | EXISTS V2: P_set_intersection2-{T}(V0,V1,V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #224: input, references = 6, size of lhs = 1:
% 11.11/11.32 #-{F} V0 | EXISTS V1: P_relation_rng-{T}(V0,V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #225: input, references = 10, size of lhs = 1:
% 11.11/11.32 #-{F} V0 | EXISTS V1: P_relation_dom-{T}(V0,V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #226: input, references = 7, size of lhs = 2:
% 11.11/11.32 #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_composition-{T}(V0,V1,V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #227: input, references = 4, size of lhs = 0:
% 11.11/11.32 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #228: input, references = 10, size of lhs = 2:
% 11.11/11.32 #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_image-{T}(V0,V1,V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 number of initial rules = 229
% 11.11/11.32
% 11.11/11.32 Simplifiers:
% 11.11/11.32 #229: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 relation_non_empty-{F}(V0), relation_non_empty-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #230: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 being_limit_ordinal-{F}(V0), being_limit_ordinal-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #231: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 ordinal_yielding-{F}(V0), ordinal_yielding-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #232: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 P_powerset-{F}(V0,V1), P_powerset-{F}(V0,V3), V1 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #233: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_omega-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #234: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 P_positive_rationals-{F}(V0), P_positive_rationals-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #235: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 P_set_intersection2-{F}(V0,V1,V2), P_set_intersection2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #236: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 P_relation_rng-{F}(V0,V1), P_relation_rng-{F}(V0,V3), V1 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #237: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V0,V3), V1 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #238: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 P_relation_composition-{F}(V0,V1,V2), P_relation_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #239: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #240: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 P_relation_image-{F}(V0,V1,V2), P_relation_image-{F}(V0,V1,V5), V2 == V5 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #241: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp1-{F}(V0,V1,V2), pppp1-{F}(V0,V4,V2), V1 == V4 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #242: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp1-{F}(V0,V1,V2), pppp1-{F}(V3,V4,V5), V2 == V5 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #243: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp2-{F}(V0,V1), pppp2-{F}(V0,V3), V1 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #244: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp3-{F}(V0), pppp3-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #245: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp4-{F}(V0), pppp4-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #246: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #247: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #248: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp7-{F}(V0), pppp7-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #249: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #250: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #251: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp10-{F}(V0), pppp10-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #252: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp11-{F}(V0), pppp11-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #253: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp12-{F}(V0,V1), pppp12-{F}(V2,V1), V0 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #254: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp13-{F}(V0), pppp13-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #255: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp14-{F}(V0,V1), pppp14-{F}(V2,V1), V0 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #256: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp14-{F}(V0,V1), pppp14-{F}(V2,V3), V1 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #257: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp15-{F}(V0,V1), pppp15-{F}(V0,V3), V1 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #258: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp15-{F}(V0,V1), pppp15-{F}(V2,V3), V0 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #259: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp16-{F}(V0,V1), pppp16-{F}(V2,V1), V0 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #260: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp17-{F}(V0,V1), pppp17-{F}(V0,V3), V1 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #261: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp18-{F}(V0), pppp18-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #262: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp19-{F}(V0), pppp19-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #263: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp20-{F}(V0), pppp20-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #264: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp21-{F}(V0), pppp21-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #265: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp22-{F}(V0), pppp22-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #266: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp23-{F}(V0,V1), pppp23-{F}(V2,V1), V0 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #267: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp24-{F}(V0), pppp24-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #268: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp25-{F}(V0,V1), pppp25-{F}(V2,V1), V0 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #269: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp25-{F}(V0,V1), pppp25-{F}(V2,V3), V1 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #270: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp26-{F}(V0,V1), pppp26-{F}(V0,V3), V1 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #271: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp26-{F}(V0,V1), pppp26-{F}(V2,V3), V0 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #272: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp27-{F}(V0,V1), pppp27-{F}(V2,V1), V0 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #273: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp28-{F}(V0), pppp28-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #274: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp29-{F}(V0), pppp29-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #275: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp30-{F}(V0), pppp30-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #276: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp31-{F}(V0), pppp31-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #277: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp32-{F}(V0), pppp32-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #278: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp33-{F}(V0), pppp33-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #279: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp34-{F}(V0,V1), pppp34-{F}(V2,V1), V0 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #280: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp34-{F}(V0,V1), pppp34-{F}(V2,V3), V1 == V3 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #281: unsound, references = 3, size of lhs = 3:
% 11.11/11.32 pppp35-{F}(V0), pppp35-{F}(V1), V0 == V1 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 number of simplifiers = 53
% 11.11/11.32
% 11.11/11.32 Learnt:
% 11.11/11.32 #285: exists( #223, #80 ), references = 1, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), #-{F} V3 | P_set_intersection2-{T}(V3,V3,V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #287: exists( #223, #25 ), references = 1, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_set_intersection2-{F}(V2,V3,V4) | P_set_intersection2-{T}(V3,V2,V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #295: mergings( V2 == V5, V3 == V6, V4 == V7; #291 ), references = 1, size of lhs = 4:
% 11.11/11.32 empty-{F}(V0), P_omega-{F}(V1), P_positive_rationals-{F}(V2), P_empty_set-{F}(V3) | P_relation_dom-{T}(V0,V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #304: mergings( V2 == V5, V3 == V6, V4 == V7; #299 ), references = 1, size of lhs = 4:
% 11.11/11.32 empty-{F}(V0), P_omega-{F}(V1), P_positive_rationals-{F}(V2), P_empty_set-{F}(V3) | P_relation_rng-{T}(V0,V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #308: mergings( V2 == V5, V3 == V6, V4 == V7; #300 ), references = 1, size of lhs = 5:
% 11.11/11.32 empty-{F}(V0), P_omega-{F}(V1), P_positive_rationals-{F}(V2), P_empty_set-{F}(V3), empty-{F}(V4) | P_relation_rng-{T}(V0,V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #310: exists( #223, #210 ), references = 1, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), #-{F} V3 | P_set_intersection2-{T}(V3,V2,V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #320: mergings( V3 == V5, V4 == V6; #316 ), references = 2, size of lhs = 5:
% 11.11/11.32 relation-{F}(V0), empty-{F}(V1), P_omega-{F}(V2), P_positive_rationals-{F}(V3), P_empty_set-{F}(V4) | P_relation_composition-{T}(V0,V1,V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #323: mergings( V3 == V5, V4 == V6; #317 ), references = 1, size of lhs = 6:
% 11.11/11.32 relation-{F}(V0), empty-{F}(V1), P_omega-{F}(V2), P_positive_rationals-{F}(V3), P_empty_set-{F}(V4), empty-{F}(V5) | P_relation_composition-{T}(V0,V1,V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #326: exists( #228, #199 ), references = 2, size of lhs = 7:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), P_relation_dom-{F}(V3,V4), P_relation_image-{F}(V3,V5,V6), P_set_intersection2-{F}(V4,V5,V7) | P_relation_image-{T}(V3,V7,V6)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #332: mergings( V3 == V6, V4 == V7, V5 == V8; #328 ), references = 1, size of lhs = 10:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), P_relation_rng-{F}(V3,V4), relation-{F}(V5), P_relation_dom-{F}(V5,V6), P_set_intersection2-{F}(V6,V7,V4), P_relation_composition-{F}(V3,V5,V8), P_relation_rng-{F}(V8,V9) | P_relation_image-{T}(V5,V7,V9)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #345: mergings( V0 == V4, V1 == V5, V2 == V6; #340 ), references = 1, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | pppp11-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #349: mergings( V0 == V4, V1 == V5, V2 == V6; #341 ), references = 1, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | pppp11-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #365: mergings( V0 == V4, V1 == V5, V2 == V6; #360 ), references = 1, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | pppp13-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #369: mergings( V0 == V4, V1 == V5, V2 == V6; #361 ), references = 1, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | pppp13-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #381: mergings( V0 == V4, V1 == V5, V2 == V6; #376 ), references = 1, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | pppp18-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #385: mergings( V0 == V4, V1 == V5, V2 == V6; #377 ), references = 1, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | pppp18-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #404: mergings( V0 == V4, V1 == V5, V2 == V6; #399 ), references = 1, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | pppp20-{T}(V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #408: mergings( V0 == V4, V1 == V5, V2 == V6; #400 ), references = 1, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | pppp20-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #422: mergings( V0 == V4, V1 == V5, V2 == V6; #418 ), references = 1, size of lhs = 3:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2) | pppp26-{T}(V1,V2)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #443: mergings( V0 == V5, V1 == V6, V2 == V7; #439 ), references = 1, size of lhs = 7:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3), P_powerset-{F}(V3,V4), element-{F}(V5,V4), element-{F}(V6,V5) | empty-{T}(V5)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #463: mergings( V0 == V5, V1 == V6, V2 == V7; #457 ), references = 1, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V3,V4), V3 == V2 | pppp36-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #468: mergings( V0 == V5, V1 == V6, V2 == V7, V3 == V7; #458 ), references = 1, size of lhs = 6:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3), V2 == V3, P_powerset-{F}(V2,V4) | pppp36-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #496: mergings( V0 == V5, V1 == V6, V2 == V7; #490 ), references = 1, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V3,V4), V3 == V2 | pppp37-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #501: mergings( V0 == V5, V1 == V6, V2 == V7, V3 == V7; #491 ), references = 1, size of lhs = 6:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3), V2 == V3, P_powerset-{F}(V2,V4) | pppp37-{T}(V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #513: disj( #211, input ), references = 1, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), element-{F}(V3,V3) | empty-{T}(V3)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #541: mergings( V0 == V4, V1 == V5, V2 == V6; #535 ), references = 1, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), element-{F}(V1,V0), P_positive_rationals-{F}(V2), P_empty_set-{F}(V3) | in-{T}(V1,V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #545: mergings( V0 == V5, V1 == V4, V2 == V6; #536 ), references = 1, size of lhs = 4:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), element-{F}(V2,V1), P_empty_set-{F}(V3) | in-{T}(V2,V1)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #549: mergings( V0 == V5, V1 == V6, V2 == V7; #537 ), references = 1, size of lhs = 5:
% 11.11/11.32 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), element-{F}(V3,V4), P_powerset-{F}(V5,V4) | in-{T}(V3,V4)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #614: exists( #225, #31 ), references = 1, size of lhs = 3:
% 11.11/11.32 P_relation_rng-{F}(V0,V1), pppp1-{F}(V2,V0,V3), V1 == V2 | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #616: exists( #224, #613 ), references = 4, size of lhs = 1:
% 11.11/11.32 pppp1-{F}(V0,V1,V2) | P_relation_rng-{T}(V1,V0)
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #694: mergings( V2 == V6, V3 == V7, V5 == V9, V4 == V8, V9 == V11; #686 ), references = 1, size of lhs = 7:
% 11.11/11.32 empty-{F}(V0), P_omega-{F}(V1), P_positive_rationals-{F}(V2), P_empty_set-{F}(V3), P_relation_rng-{F}(V4,V0), P_powerset-{F}(V5,V4), pppp1-{F}(V0,V4,V6) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #700: mergings( V2 == V7, V3 == V8, V5 == V6, V4 == V9, V6 == V10; #687 ), references = 1, size of lhs = 7:
% 11.11/11.32 empty-{F}(V0), P_relation_rng-{F}(V1,V0), P_omega-{F}(V2), P_positive_rationals-{F}(V3), P_empty_set-{F}(V4), V1 == V4, pppp1-{F}(V0,V1,V5) | FALSE
% 11.11/11.32 (used 0 times, uses = {})
% 11.11/11.32
% 11.11/11.32 #707: mergings( V2 == V6, V3 == V7, V5 == V9, V4 == V8, V9 == V11, V0 == V8; #688 ), references = 1, size of lhs = 7:
% 11.11/11.33 empty-{F}(V0), P_omega-{F}(V1), P_positive_rationals-{F}(V2), P_empty_set-{F}(V3), P_relation_rng-{F}(V3,V0), in-{F}(V4,V3), pppp1-{F}(V0,V3,V5) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #717: mergings( V0 == V4, V4 == V7, V1 == V5, V5 == V8, V6 == V9; #711 ), references = 1, size of lhs = 5:
% 11.11/11.33 pppp0-{F}(V0), empty-{F}(V0), P_omega-{F}(V1), P_positive_rationals-{F}(V2), P_empty_set-{F}(V3) | pppp1-{T}(V0,V3,V1)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #751: mergings( V0 == V6, V1 == V7, V2 == V8; #747 ), references = 1, size of lhs = 4:
% 11.11/11.33 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V3,V4) | pppp17-{T}(V4,V2)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #781: mergings( V0 == V6, V1 == V7, V2 == V8; #777 ), references = 1, size of lhs = 4:
% 11.11/11.33 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), P_powerset-{F}(V3,V4) | pppp23-{T}(V2,V4)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #835: disj( #211, input ), references = 1, size of lhs = 5:
% 11.11/11.33 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), element-{F}(V3,V4), in-{F}(V4,V3) | empty-{T}(V4)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #891: exists( #228, #201 ), references = 1, size of lhs = 8:
% 11.11/11.33 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), P_relation_rng-{F}(V3,V4), relation-{F}(V5), P_relation_composition-{F}(V3,V5,V6), P_relation_rng-{F}(V6,V7) | P_relation_image-{T}(V5,V4,V7)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #929: exists( #228, #199 ), references = 1, size of lhs = 7:
% 11.11/11.33 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), P_relation_dom-{F}(V3,V4), P_set_intersection2-{F}(V4,V5,V6), P_relation_image-{F}(V3,V6,V7) | P_relation_image-{T}(V3,V5,V7)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #931: exists( #228, #201 ), references = 1, size of lhs = 8:
% 11.11/11.33 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), P_relation_rng-{F}(V3,V4), relation-{F}(V5), P_relation_composition-{F}(V3,V5,V6), P_relation_rng-{F}(V6,V7) | P_relation_image-{T}(V5,V4,V7)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #939: mergings( V3 == V6, V4 == V7, V5 == V8; #935 ), references = 1, size of lhs = 5:
% 11.11/11.33 relation-{F}(V0), empty-{F}(V1), P_omega-{F}(V2), P_positive_rationals-{F}(V3), P_empty_set-{F}(V4) | P_relation_composition-{T}(V1,V0,V4)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #969: exists( #224, #201 ), references = 3, size of lhs = 8:
% 11.11/11.33 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), P_relation_rng-{F}(V3,V4), relation-{F}(V5), P_relation_composition-{F}(V3,V5,V6), P_relation_image-{F}(V5,V4,V7) | P_relation_rng-{T}(V6,V7)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #974: exists( #225, #214 ), references = 3, size of lhs = 10:
% 11.11/11.33 P_omega-{F}(V0), P_positive_rationals-{F}(V1), P_empty_set-{F}(V2), relation-{F}(V3), P_relation_rng-{F}(V3,V4), P_relation_dom-{F}(V3,V5), relation-{F}(V6), P_relation_dom-{F}(V6,V7), subset-{F}(V4,V7), P_relation_composition-{F}(V3,V6,V8) | P_relation_dom-{T}(V8,V5)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1087: mergings( V3 == V6, V6 == V9, V9 == V15, V15 == V20, V4 == V7, V7 == V10, V10 == V16, V16 == V21, V12 == V18, V8 == V11, V11 == V17, V17 == V22; #1074 ), references = 1, size of lhs = 16:
% 11.11/11.33 empty-{F}(V0), relation-{F}(V0), relation-{F}(V1), P_relation_dom-{F}(V1,V2), P_relation_rng-{F}(V1,V3), subset-{F}(V3,V4), relation-{F}(V5), P_relation_dom-{F}(V5,V4), P_relation_image-{F}(V5,V3,V6), P_omega-{F}(V7), P_positive_rationals-{F}(V8), P_empty_set-{F}(V9), P_relation_dom-{F}(V0,V10), subset-{F}(V6,V10), P_relation_dom-{F}(V9,V11), V11 == V2 | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1104: mergings( V2 == V5, V5 == V8, V8 == V11, V11 == V16, V3 == V6, V6 == V9, V9 == V12, V12 == V17, V21 == V22, V22 == V23, V7 == V10, V10 == V13, V13 == V18, V23 == V25; #1089 ), references = 3, size of lhs = 14:
% 11.11/11.33 empty-{F}(V0), relation-{F}(V0), relation-{F}(V1), P_relation_dom-{F}(V1,V2), P_omega-{F}(V3), P_positive_rationals-{F}(V4), P_empty_set-{F}(V5), P_relation_dom-{F}(V0,V6), P_relation_dom-{F}(V5,V7), subset-{F}(V8,V2), P_relation_rng-{F}(V9,V8), P_relation_image-{F}(V1,V8,V10), subset-{F}(V10,V6), pppp1-{F}(V8,V9,V11) | P_relation_dom-{T}(V9,V7)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1134: mergings( V0 == V7, V7 == V12, V12 == V15, V1 == V8, V8 == V13, V13 == V16, V9 == V14, V14 == V17; #1124 ), references = 1, size of lhs = 14:
% 11.11/11.33 pppp0-{F}(V0), empty-{F}(V1), relation-{F}(V1), relation-{F}(V2), P_relation_dom-{F}(V2,V3), subset-{F}(V0,V3), P_relation_dom-{F}(V1,V4), empty-{F}(V5), P_omega-{F}(V6), P_positive_rationals-{F}(V7), P_empty_set-{F}(V8), P_relation_dom-{F}(V8,V5), P_relation_image-{F}(V2,V0,V9), subset-{F}(V9,V4) | pppp1-{T}(V0,V8,V6)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1143: mergings( V0 == V7, V7 == V12, V12 == V15, V1 == V8, V8 == V13, V13 == V16, V9 == V14, V14 == V17; #1125 ), references = 1, size of lhs = 15:
% 11.11/11.33 pppp0-{F}(V0), empty-{F}(V1), relation-{F}(V1), relation-{F}(V2), P_relation_dom-{F}(V2,V3), subset-{F}(V0,V3), P_relation_dom-{F}(V1,V4), empty-{F}(V5), P_omega-{F}(V6), P_positive_rationals-{F}(V7), P_empty_set-{F}(V8), P_relation_dom-{F}(V8,V5), empty-{F}(V9), P_relation_image-{F}(V2,V0,V10), subset-{F}(V10,V4) | pppp1-{T}(V0,V9,V6)
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1248: mergings( V3 == V5, V5 == V8, V8 == V13, V13 == V19, V19 == V21, V4 == V6, V6 == V9, V9 == V14, V14 == V20, V20 == V22, V11 == V16, V7 == V10, V10 == V15; #1234 ), references = 2, size of lhs = 15:
% 11.11/11.33 function-{F}(V0), relation-{F}(V0), function-{F}(V1), relation-{F}(V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V1,V3), P_relation_image-{F}(V0,V3,V4), P_relation_dom-{F}(V1,V5), P_relation_dom-{F}(V0,V6), subset-{F}(V3,V6), in-{F}(V5,V7), P_omega-{F}(V7), P_positive_rationals-{F}(V8), pppp34-{F}(V9,V10), P_relation_image-{F}(V10,V9,V4) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1263: mergings( V7 == V8, V8 == V9, V9 == V12, V5 == V14, V14 == V16, V12 == V11, V11 == V13, V13 == V15; #1254 ), references = 1, size of lhs = 12:
% 11.11/11.33 function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), P_omega-{F}(V3), P_positive_rationals-{F}(V4), subset-{F}(V5,V2), P_relation_image-{F}(V0,V5,V6), P_relation_rng-{F}(V7,V5), pppp1-{F}(V5,V7,V3), pppp34-{F}(V8,V9), P_relation_image-{F}(V9,V8,V6) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1267: mergings( V1 == V7; #1265 ), references = 2, size of lhs = 11:
% 11.11/11.33 pppp0-{F}(V0), function-{F}(V1), relation-{F}(V1), P_empty_set-{F}(V2), P_relation_dom-{F}(V1,V3), subset-{F}(V0,V3), P_omega-{F}(V4), P_positive_rationals-{F}(V5), P_relation_image-{F}(V1,V0,V6), pppp34-{F}(V7,V8), P_relation_image-{F}(V8,V7,V6) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1274: mergings( V3 == V8, V4 == V5, V5 == V9; #1270 ), references = 1, size of lhs = 8:
% 11.11/11.33 function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), subset-{F}(V3,V2), pppp34-{F}(V3,V0), P_omega-{F}(V4), P_positive_rationals-{F}(V5) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1352: mergings( V3 == V6, V6 == V8, V8 == V13, V4 == V7, V7 == V9, V9 == V14, V10 == V12, V5 == V11; #1343 ), references = 1, size of lhs = 10:
% 11.11/11.33 function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), P_omega-{F}(V3), P_positive_rationals-{F}(V4), pppp34-{F}(V5,V0), P_set_intersection2-{F}(V2,V5,V6), subset-{F}(V6,V2), P_set_intersection2-{F}(V7,V5,V6) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1365: mergings( V3 == V6, V6 == V9, V9 == V11, V11 == V15, V4 == V7, V7 == V10, V10 == V12, V12 == V16, V5 == V8, V8 == V14; #1354 ), references = 1, size of lhs = 7:
% 11.11/11.33 function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), P_omega-{F}(V3), P_positive_rationals-{F}(V4), pppp34-{F}(V5,V0) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1377: mergings( V2 == V5, V5 == V8, V8 == V10, V10 == V14, V3 == V6, V6 == V9, V9 == V11, V11 == V15, V4 == V7, V7 == V12; #1366 ), references = 1, size of lhs = 7:
% 11.11/11.33 pppp35-{F}(V0), function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), P_omega-{F}(V3), P_positive_rationals-{F}(V4) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1389: mergings( V2 == V5, V5 == V8, V8 == V10, V10 == V13, V3 == V6, V6 == V9, V9 == V11, V11 == V14, V4 == V7, V7 == V12; #1378 ), references = 2, size of lhs = 6:
% 11.11/11.33 pppp35-{F}(V0), function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_omega-{F}(V2), P_positive_rationals-{F}(V3) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1420: mergings( V0 == V5, V1 == V6, V2 == V4; #1416 ), references = 1, size of lhs = 3:
% 11.11/11.33 P_empty_set-{F}(V0), P_omega-{F}(V1), P_positive_rationals-{F}(V2) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1424: mergings( V1 == V3, V2 == V4; #1421 ), references = 1, size of lhs = 2:
% 11.11/11.33 P_omega-{F}(V0), P_positive_rationals-{F}(V1) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1427: mergings( V1 == V2; #1425 ), references = 1, size of lhs = 1:
% 11.11/11.33 P_omega-{F}(V0) | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 #1429: exists( #221, #1425 ), references = 1, size of lhs = 0:
% 11.11/11.33 FALSE | FALSE
% 11.11/11.33 (used 0 times, uses = {})
% 11.11/11.33
% 11.11/11.33 number of learnt formulas = 59
% 11.11/11.33
% 11.11/11.33
% 11.11/11.33 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.11/11.33
% 11.11/11.33 randbase = 1
%------------------------------------------------------------------------------