%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SEU296+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n009.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 49.67s 49.89s
% Output : Refutation 49.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU296+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.34 % Computer : n009.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 18:48:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 49.67/49.89 GeoParameters:
% 49.67/49.89
% 49.67/49.89 tptp_input = 1
% 49.67/49.89 tptp_output = 0
% 49.67/49.89 nonempty = 1
% 49.67/49.89 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.67/49.89 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 49.67/49.89
% 49.67/49.89
% 49.67/49.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.67/49.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.67/49.89
% 49.67/49.89 RuleSystem INPUT:
% 49.67/49.89
% 49.67/49.89 Initial Rules:
% 49.67/49.89 #0: input, references = 3, size of lhs = 2:
% 49.67/49.89 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #1: input, references = 3, size of lhs = 2:
% 49.67/49.89 ordinal-{F}(V0), element-{F}(V1,V0) | epsilon_transitive-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #2: input, references = 3, size of lhs = 2:
% 49.67/49.89 ordinal-{F}(V0), element-{F}(V1,V0) | epsilon_connected-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #3: input, references = 3, size of lhs = 2:
% 49.67/49.89 ordinal-{F}(V0), element-{F}(V1,V0) | ordinal-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #4: input, references = 3, size of lhs = 1:
% 49.67/49.89 empty-{F}(V0) | finite-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #5: input, references = 3, size of lhs = 1:
% 49.67/49.89 empty-{F}(V0) | function-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #6: input, references = 3, size of lhs = 1:
% 49.67/49.89 ordinal-{F}(V0) | epsilon_transitive-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #7: input, references = 3, size of lhs = 1:
% 49.67/49.89 ordinal-{F}(V0) | epsilon_connected-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #8: input, references = 3, size of lhs = 1:
% 49.67/49.89 empty-{F}(V0) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #9: input, references = 3, size of lhs = 2:
% 49.67/49.89 empty-{F}(V0), ordinal-{F}(V0) | epsilon_transitive-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #10: input, references = 3, size of lhs = 2:
% 49.67/49.89 empty-{F}(V0), ordinal-{F}(V0) | epsilon_connected-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #11: input, references = 3, size of lhs = 2:
% 49.67/49.89 empty-{F}(V0), ordinal-{F}(V0) | natural-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #12: input, references = 3, size of lhs = 3:
% 49.67/49.89 P_powerset-{F}(V0,V1), finite-{F}(V0), element-{F}(V2,V1) | finite-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #13: input, references = 3, size of lhs = 3:
% 49.67/49.89 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #14: input, references = 3, size of lhs = 2:
% 49.67/49.89 epsilon_transitive-{F}(V0), epsilon_connected-{F}(V0) | ordinal-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #15: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), element-{F}(V1,V0) | epsilon_transitive-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #16: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), element-{F}(V1,V0) | epsilon_connected-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #17: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), element-{F}(V1,V0) | ordinal-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #18: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), element-{F}(V1,V0) | natural-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #19: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), empty-{F}(V1) | epsilon_transitive-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #20: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), empty-{F}(V1) | epsilon_connected-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #21: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), empty-{F}(V1) | ordinal-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #22: input, references = 4, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_set_intersection2-{F}(V1,V2,V3), P_set_intersection2-{F}(V2,V1,V4), V3 == V4 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #23: input, references = 7, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), finite-{F}(V1) | pppp0-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #24: input, references = 4, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), pppp0-{F}(V1) | finite-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #25: input, references = 5, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), pppp0-{F}(V1) | EXISTS V2: pppp1-{T}(V1,V2,V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #26: input, references = 4, size of lhs = 6:
% 49.67/49.89 P_omega-{F}(V0), P_relation_rng-{F}(V2,V1), P_relation_dom-{F}(V2,V4), relation-{F}(V2), function-{F}(V2), in-{F}(V4,V0) | pppp0-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #27: input, references = 5, size of lhs = 3:
% 49.67/49.89 pppp1-{F}(V0,V1,V2), P_relation_rng-{F}(V1,V3), P_relation_dom-{F}(V1,V4) | in-{T}(V4,V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #28: input, references = 4, size of lhs = 4:
% 49.67/49.89 pppp1-{F}(V0,V1,V2), P_relation_rng-{F}(V1,V3), P_relation_dom-{F}(V1,V4), V3 == V0 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #29: input, references = 5, size of lhs = 3:
% 49.67/49.89 pppp1-{F}(V0,V1,V2), P_relation_rng-{F}(V1,V3), P_relation_dom-{F}(V1,V4) | function-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #30: input, references = 8, size of lhs = 3:
% 49.67/49.89 pppp1-{F}(V0,V1,V2), P_relation_rng-{F}(V1,V3), P_relation_dom-{F}(V1,V4) | relation-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #31: input, references = 7, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), relation-{F}(V2) | relation-{T}(V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #32: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), #-{F} V1 | EXISTS V2: pppp2-{T}(V1,V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #33: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp2-{F}(V0,V1) | element-{T}(V1,V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #34: input, references = 7, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), finite-{F}(V1), P_set_intersection2-{F}(V2,V1,V3) | finite-{T}(V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #35: input, references = 5, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V1,V2,V3), empty-{F}(V2) | empty-{T}(V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #36: input, references = 3, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V1,V2,V3), empty-{F}(V2) | relation-{T}(V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #37: input, references = 3, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), finite-{F}(V1), P_set_intersection2-{F}(V1,V2,V3) | finite-{T}(V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #38: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | empty-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #39: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | relation-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #40: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | relation_empty_yielding-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #41: input, references = 3, size of lhs = 7:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V3,V2,V4), relation-{F}(V3), function-{F}(V3) | relation-{T}(V4)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #42: input, references = 5, size of lhs = 7:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V3,V2,V4), relation-{F}(V3), function-{F}(V3) | function-{T}(V4)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #43: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | epsilon_transitive-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #44: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | epsilon_connected-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #45: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | ordinal-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #46: input, references = 3, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V0) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #47: input, references = 3, size of lhs = 5:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), P_set_intersection2-{F}(V3,V2,V4), relation-{F}(V3) | relation-{T}(V4)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #48: input, references = 4, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V3), empty-{F}(V3) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #49: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | empty-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #50: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | pppp3-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #51: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp3-{F}(V0) | ordinal-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #52: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp3-{F}(V0) | epsilon_connected-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #53: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp3-{F}(V0) | epsilon_transitive-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #54: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp3-{F}(V0) | empty-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #55: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp3-{F}(V0) | one_to_one-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #56: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp3-{F}(V0) | function-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #57: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp3-{F}(V0) | relation_empty_yielding-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #58: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp3-{F}(V0) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #59: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | empty-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #60: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | relation-{T}(V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #61: input, references = 3, size of lhs = 5:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V2,V3), relation-{F}(V2), empty-{F}(V3) | empty-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #62: input, references = 7, size of lhs = 5:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_relation_rng-{F}(V2,V3), relation-{F}(V2), empty-{F}(V3) | empty-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #63: input, references = 5, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V2,V3), empty-{F}(V2) | empty-{T}(V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #64: input, references = 3, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V2,V3), empty-{F}(V2) | relation-{T}(V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #65: input, references = 5, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_relation_rng-{F}(V2,V3), empty-{F}(V2) | empty-{T}(V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #66: input, references = 3, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_relation_rng-{F}(V2,V3), empty-{F}(V2) | relation-{T}(V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #67: input, references = 5, size of lhs = 5:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), P_relation_composition-{F}(V3,V2,V4), empty-{F}(V3) | empty-{T}(V4)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #68: input, references = 3, size of lhs = 5:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), P_relation_composition-{F}(V3,V2,V4), empty-{F}(V3) | relation-{T}(V4)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #69: input, references = 4, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_set_intersection2-{F}(V2,V2,V3), V3 == V2 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #70: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp5-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #71: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp5-{F}(V0) | pppp4-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #72: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp4-{F}(V0) | natural-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #73: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp4-{F}(V0) | ordinal-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #74: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp4-{F}(V0) | epsilon_connected-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #75: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp4-{F}(V0) | epsilon_transitive-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #76: input, references = 3, size of lhs = 2:
% 49.67/49.89 pppp4-{F}(V0), empty-{F}(V0) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #77: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp6-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #78: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp6-{F}(V0) | finite-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #79: input, references = 3, size of lhs = 2:
% 49.67/49.89 pppp6-{F}(V0), empty-{F}(V0) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #80: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp7-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #81: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp7-{F}(V0) | function-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #82: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp7-{F}(V0) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #83: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp8-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #84: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp8-{F}(V0) | ordinal-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #85: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp8-{F}(V0) | epsilon_connected-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #86: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp8-{F}(V0) | epsilon_transitive-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #87: input, references = 4, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp9-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #88: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp9-{F}(V0) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #89: input, references = 5, size of lhs = 1:
% 49.67/49.89 pppp9-{F}(V0) | empty-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #90: input, references = 4, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V3) | empty-{T}(V2), pppp27-{T}(V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #91: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp27-{F}(V0) | EXISTS V1: pppp10-{T}(V1,V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #92: input, references = 3, size of lhs = 2:
% 49.67/49.89 pppp10-{F}(V0,V1), empty-{F}(V0) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #93: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp10-{F}(V0,V1) | element-{T}(V0,V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #94: input, references = 4, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp11-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #95: input, references = 5, size of lhs = 1:
% 49.67/49.89 pppp11-{F}(V0) | empty-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #96: input, references = 4, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V3) | EXISTS V4: pppp13-{T}(V3,V4)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #97: input, references = 4, size of lhs = 1:
% 49.67/49.89 pppp13-{F}(V0,V1) | pppp12-{T}(V1,V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #98: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp12-{F}(V0,V1) | finite-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #99: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp12-{F}(V0,V1) | natural-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #100: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp12-{F}(V0,V1) | ordinal-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #101: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp12-{F}(V0,V1) | epsilon_connected-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #102: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp12-{F}(V0,V1) | epsilon_transitive-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #103: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp12-{F}(V0,V1) | one_to_one-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #104: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp12-{F}(V0,V1) | function-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #105: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp12-{F}(V0,V1) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #106: input, references = 4, size of lhs = 1:
% 49.67/49.89 pppp12-{F}(V0,V1) | empty-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #107: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp12-{F}(V0,V1) | element-{T}(V0,V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #108: input, references = 4, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp14-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #109: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp14-{F}(V0) | function-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #110: input, references = 5, size of lhs = 1:
% 49.67/49.89 pppp14-{F}(V0) | empty-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #111: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp14-{F}(V0) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #112: input, references = 4, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp16-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #113: input, references = 5, size of lhs = 1:
% 49.67/49.89 pppp16-{F}(V0) | pppp15-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #114: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp15-{F}(V0) | ordinal-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #115: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp15-{F}(V0) | epsilon_connected-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #116: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp15-{F}(V0) | epsilon_transitive-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #117: input, references = 5, size of lhs = 1:
% 49.67/49.89 pppp15-{F}(V0) | empty-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #118: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp15-{F}(V0) | one_to_one-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #119: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp15-{F}(V0) | function-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #120: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp15-{F}(V0) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #121: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp17-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #122: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp17-{F}(V0) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #123: input, references = 3, size of lhs = 2:
% 49.67/49.89 pppp17-{F}(V0), empty-{F}(V0) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #124: input, references = 4, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V3) | EXISTS V4: pppp18-{T}(V4,V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #125: input, references = 4, size of lhs = 1:
% 49.67/49.89 pppp18-{F}(V0,V1) | empty-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #126: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp18-{F}(V0,V1) | element-{T}(V0,V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #127: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp19-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #128: input, references = 3, size of lhs = 2:
% 49.67/49.89 pppp19-{F}(V0), empty-{F}(V0) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #129: input, references = 4, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V3) | empty-{T}(V2), pppp28-{T}(V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #130: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp28-{F}(V0) | EXISTS V1: pppp20-{T}(V1,V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #131: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp20-{F}(V0,V1) | finite-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #132: input, references = 3, size of lhs = 2:
% 49.67/49.89 pppp20-{F}(V0,V1), empty-{F}(V0) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #133: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp20-{F}(V0,V1) | element-{T}(V0,V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #134: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp21-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #135: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp21-{F}(V0) | one_to_one-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #136: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp21-{F}(V0) | function-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #137: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp21-{F}(V0) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #138: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp22-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #139: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp22-{F}(V0) | ordinal-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #140: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp22-{F}(V0) | epsilon_connected-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #141: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp22-{F}(V0) | epsilon_transitive-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #142: input, references = 3, size of lhs = 2:
% 49.67/49.89 pppp22-{F}(V0), empty-{F}(V0) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #143: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp23-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #144: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp23-{F}(V0) | relation_empty_yielding-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #145: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp23-{F}(V0) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #146: input, references = 3, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp24-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #147: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp24-{F}(V0) | function-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #148: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp24-{F}(V0) | relation_empty_yielding-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #149: input, references = 3, size of lhs = 1:
% 49.67/49.89 pppp24-{F}(V0) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #150: input, references = 3, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), #-{F} V2 | subset-{T}(V2,V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #151: input, references = 5, size of lhs = 8:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V2,V3), relation-{F}(V2), P_relation_image-{F}(V2,V4,V5), P_set_intersection2-{F}(V3,V4,V6), P_relation_image-{F}(V2,V6,V7), V5 == V7 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #152: input, references = 3, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), finite-{F}(V2), P_set_intersection2-{F}(V2,V3,V4) | finite-{T}(V4)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #153: input, references = 7, size of lhs = 9:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_relation_rng-{F}(V2,V3), relation-{F}(V2), P_relation_composition-{F}(V2,V4,V5), P_relation_rng-{F}(V5,V6), P_relation_image-{F}(V4,V3,V7), relation-{F}(V4), V6 == V7 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #154: input, references = 4, size of lhs = 2:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1) | EXISTS V2: pppp26-{T}(V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #155: input, references = 5, size of lhs = 1:
% 49.67/49.89 pppp26-{F}(V0) | EXISTS V1: pppp25-{T}(V1,V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #156: input, references = 4, size of lhs = 1:
% 49.67/49.89 pppp26-{F}(V0) | function-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #157: input, references = 4, size of lhs = 1:
% 49.67/49.89 pppp26-{F}(V0) | relation-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #158: input, references = 4, size of lhs = 3:
% 49.67/49.89 pppp25-{F}(V0,V1), P_relation_image-{F}(V1,V0,V2), finite-{F}(V2) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #159: input, references = 6, size of lhs = 2:
% 49.67/49.89 pppp25-{F}(V0,V1), P_relation_image-{F}(V1,V0,V2) | finite-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #160: input, references = 5, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_set_intersection2-{F}(V2,V3,V4) | subset-{T}(V4,V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #161: input, references = 3, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), in-{F}(V2,V3) | element-{T}(V2,V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #162: input, references = 4, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_set_intersection2-{F}(V2,V1,V3), V3 == V1 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #163: input, references = 5, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), element-{F}(V3,V2) | empty-{T}(V2), in-{T}(V3,V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #164: input, references = 3, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V3,V4), element-{F}(V2,V4) | subset-{T}(V2,V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #165: input, references = 3, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V3,V4), subset-{F}(V2,V3) | element-{T}(V2,V4)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #166: input, references = 5, size of lhs = 11:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_relation_rng-{F}(V2,V3), P_relation_dom-{F}(V2,V4), relation-{F}(V2), P_relation_dom-{F}(V5,V6), P_relation_composition-{F}(V2,V5,V7), P_relation_dom-{F}(V7,V8), relation-{F}(V5), subset-{F}(V3,V6), V8 == V4 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #167: input, references = 3, size of lhs = 5:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V3,V4), element-{F}(V2,V4), in-{F}(V5,V2) | element-{T}(V5,V3)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #168: input, references = 3, size of lhs = 6:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V3), empty-{F}(V2), element-{F}(V4,V3), in-{F}(V5,V4) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #169: input, references = 15, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #170: input, references = 4, size of lhs = 4:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2), in-{F}(V3,V2) | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #171: input, references = 11, size of lhs = 5:
% 49.67/49.89 P_omega-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2), empty-{F}(V3), V3 == V2 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #172: input, references = 3, size of lhs = 1:
% 49.67/49.89 #-{F} V0 | EXISTS V1: P_powerset-{T}(V0,V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #173: input, references = 4, size of lhs = 0:
% 49.67/49.89 FALSE | EXISTS V0: P_omega-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #174: input, references = 8, size of lhs = 2:
% 49.67/49.89 #-{F} V0, #-{F} V1 | EXISTS V2: P_set_intersection2-{T}(V0,V1,V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #175: input, references = 6, size of lhs = 1:
% 49.67/49.89 #-{F} V0 | EXISTS V1: P_relation_rng-{T}(V0,V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #176: input, references = 11, size of lhs = 1:
% 49.67/49.89 #-{F} V0 | EXISTS V1: P_relation_dom-{T}(V0,V1)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #177: input, references = 9, size of lhs = 2:
% 49.67/49.89 #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_composition-{T}(V0,V1,V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #178: input, references = 4, size of lhs = 0:
% 49.67/49.89 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #179: input, references = 10, size of lhs = 2:
% 49.67/49.89 #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_image-{T}(V0,V1,V2)
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 number of initial rules = 180
% 49.67/49.89
% 49.67/49.89 Simplifiers:
% 49.67/49.89 #180: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 P_powerset-{F}(V0,V1), P_powerset-{F}(V0,V3), V1 == V3 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #181: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 P_omega-{F}(V0), P_omega-{F}(V1), V0 == V1 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #182: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 P_set_intersection2-{F}(V0,V1,V2), P_set_intersection2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #183: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 P_relation_rng-{F}(V0,V1), P_relation_rng-{F}(V0,V3), V1 == V3 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #184: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V0,V3), V1 == V3 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #185: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 P_relation_composition-{F}(V0,V1,V2), P_relation_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #186: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #187: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 P_relation_image-{F}(V0,V1,V2), P_relation_image-{F}(V0,V1,V5), V2 == V5 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #188: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 pppp1-{F}(V0,V1,V2), pppp1-{F}(V0,V4,V2), V1 == V4 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #189: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 pppp1-{F}(V0,V1,V2), pppp1-{F}(V3,V4,V5), V2 == V5 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #190: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 pppp2-{F}(V0,V1), pppp2-{F}(V0,V3), V1 == V3 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #191: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 pppp3-{F}(V0), pppp3-{F}(V1), V0 == V1 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #192: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 pppp4-{F}(V0), pppp4-{F}(V1), V0 == V1 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #193: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #194: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #195: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 pppp7-{F}(V0), pppp7-{F}(V1), V0 == V1 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.89
% 49.67/49.89 #196: unsound, references = 3, size of lhs = 3:
% 49.67/49.89 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 49.67/49.89 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #197: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #198: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp10-{F}(V0,V1), pppp10-{F}(V2,V1), V0 == V2 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #199: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp11-{F}(V0), pppp11-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #200: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp12-{F}(V0,V1), pppp12-{F}(V2,V1), V0 == V2 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #201: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp13-{F}(V0,V1), pppp13-{F}(V0,V3), V1 == V3 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #202: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp14-{F}(V0), pppp14-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #203: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp15-{F}(V0), pppp15-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #204: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp16-{F}(V0), pppp16-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #205: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp17-{F}(V0), pppp17-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #206: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp18-{F}(V0,V1), pppp18-{F}(V2,V1), V0 == V2 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #207: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp19-{F}(V0), pppp19-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #208: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp20-{F}(V0,V1), pppp20-{F}(V2,V1), V0 == V2 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #209: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp21-{F}(V0), pppp21-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #210: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp22-{F}(V0), pppp22-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #211: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp23-{F}(V0), pppp23-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #212: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp24-{F}(V0), pppp24-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #213: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp25-{F}(V0,V1), pppp25-{F}(V2,V1), V0 == V2 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #214: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp25-{F}(V0,V1), pppp25-{F}(V2,V3), V1 == V3 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #215: unsound, references = 3, size of lhs = 3:
% 49.67/49.90 pppp26-{F}(V0), pppp26-{F}(V1), V0 == V1 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 number of simplifiers = 36
% 49.67/49.90
% 49.67/49.90 Learnt:
% 49.67/49.90 #218: exists( #174, #69 ), references = 1, size of lhs = 3:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), #-{F} V2 | P_set_intersection2-{T}(V2,V2,V2)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #220: exists( #174, #22 ), references = 2, size of lhs = 2:
% 49.67/49.90 P_omega-{F}(V0), P_set_intersection2-{F}(V1,V2,V3) | P_set_intersection2-{T}(V2,V1,V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #222: exists( #174, #162 ), references = 1, size of lhs = 3:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), #-{F} V2 | P_set_intersection2-{T}(V2,V1,V1)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #230: mergings( V2 == V4, V3 == V5; #226 ), references = 1, size of lhs = 3:
% 49.67/49.90 empty-{F}(V0), P_omega-{F}(V1), P_empty_set-{F}(V2) | P_relation_rng-{T}(V0,V2)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #233: mergings( V2 == V4, V3 == V5; #227 ), references = 1, size of lhs = 4:
% 49.67/49.90 empty-{F}(V0), P_omega-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_rng-{T}(V0,V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #241: mergings( V2 == V4, V3 == V5; #237 ), references = 1, size of lhs = 3:
% 49.67/49.90 empty-{F}(V0), P_omega-{F}(V1), P_empty_set-{F}(V2) | P_relation_dom-{T}(V0,V2)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #244: mergings( V2 == V4, V3 == V5; #238 ), references = 1, size of lhs = 4:
% 49.67/49.90 empty-{F}(V0), P_omega-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_dom-{T}(V0,V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #251: mergings( V3 == V4; #248 ), references = 2, size of lhs = 4:
% 49.67/49.90 relation-{F}(V0), empty-{F}(V1), P_omega-{F}(V2), P_empty_set-{F}(V3) | P_relation_composition-{T}(V0,V1,V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #253: mergings( V3 == V4; #249 ), references = 1, size of lhs = 5:
% 49.67/49.90 relation-{F}(V0), empty-{F}(V1), P_omega-{F}(V2), P_empty_set-{F}(V3), empty-{F}(V4) | P_relation_composition-{T}(V0,V1,V4)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #259: exists( #179, #153 ), references = 1, size of lhs = 7:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), P_relation_rng-{F}(V2,V3), relation-{F}(V4), P_relation_composition-{F}(V2,V4,V5), P_relation_rng-{F}(V5,V6) | P_relation_image-{T}(V4,V3,V6)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #262: exists( #179, #151 ), references = 1, size of lhs = 6:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), P_relation_dom-{F}(V2,V3), P_set_intersection2-{F}(V3,V4,V5), P_relation_image-{F}(V2,V5,V6) | P_relation_image-{T}(V2,V4,V6)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #275: mergings( V0 == V3, V1 == V4; #271 ), references = 1, size of lhs = 2:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1) | pppp9-{T}(V1)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #278: mergings( V0 == V3, V1 == V4; #272 ), references = 1, size of lhs = 3:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | pppp9-{T}(V2)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #287: mergings( V0 == V3, V1 == V4; #283 ), references = 1, size of lhs = 2:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1) | pppp14-{T}(V1)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #290: mergings( V0 == V3, V1 == V4; #284 ), references = 1, size of lhs = 3:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | pppp14-{T}(V2)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #304: mergings( V0 == V3, V1 == V4; #300 ), references = 1, size of lhs = 2:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1) | pppp11-{T}(V1)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #307: mergings( V0 == V3, V1 == V4; #301 ), references = 1, size of lhs = 3:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | pppp11-{T}(V2)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #319: mergings( V0 == V3, V1 == V4; #315 ), references = 1, size of lhs = 2:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1) | pppp16-{T}(V1)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #322: mergings( V0 == V3, V1 == V4; #316 ), references = 1, size of lhs = 3:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | pppp16-{T}(V2)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #330: mergings( V0 == V4, V1 == V5; #325 ), references = 1, size of lhs = 4:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V3), V2 == V1 | pppp27-{T}(V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #334: mergings( V0 == V4, V1 == V5, V2 == V5; #326 ), references = 1, size of lhs = 5:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2), V1 == V2, P_powerset-{F}(V1,V3) | pppp27-{T}(V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #338: mergings( V0 == V4, V1 == V5, V2 == V5; #327 ), references = 1, size of lhs = 4:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V1), P_powerset-{F}(V1,V3) | pppp27-{T}(V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #349: mergings( V0 == V4, V1 == V5; #344 ), references = 1, size of lhs = 4:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V3), V2 == V1 | pppp28-{T}(V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #353: mergings( V0 == V4, V1 == V5, V2 == V5; #345 ), references = 1, size of lhs = 5:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2), V1 == V2, P_powerset-{F}(V1,V3) | pppp28-{T}(V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #357: mergings( V0 == V4, V1 == V5, V2 == V5; #346 ), references = 1, size of lhs = 4:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V1), P_powerset-{F}(V1,V3) | pppp28-{T}(V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #368: mergings( V0 == V4, V1 == V5; #365 ), references = 1, size of lhs = 6:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2), P_powerset-{F}(V2,V3), element-{F}(V4,V3), element-{F}(V5,V4) | empty-{T}(V4)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #390: mergings( V0 == V3, V1 == V4; #385 ), references = 1, size of lhs = 3:
% 49.67/49.90 P_omega-{F}(V0), element-{F}(V1,V0), P_empty_set-{F}(V2) | in-{T}(V1,V0)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #393: mergings( V0 == V4, V1 == V5; #386 ), references = 1, size of lhs = 4:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), element-{F}(V2,V3), P_powerset-{F}(V4,V3) | in-{T}(V2,V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #396: mergings( V0 == V4, V1 == V5; #387 ), references = 1, size of lhs = 4:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), element-{F}(V2,V3), V3 == V1 | in-{T}(V2,V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #435: mergings( V0 == V5, V1 == V6; #432 ), references = 1, size of lhs = 3:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V3) | pppp13-{T}(V3,V1)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #465: mergings( V0 == V5, V1 == V6; #462 ), references = 1, size of lhs = 3:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V2,V3) | pppp18-{T}(V1,V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #475: exists( #176, #28 ), references = 1, size of lhs = 3:
% 49.67/49.90 P_relation_rng-{F}(V0,V1), pppp1-{F}(V2,V0,V3), V1 == V2 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #477: exists( #175, #474 ), references = 3, size of lhs = 1:
% 49.67/49.90 pppp1-{F}(V0,V1,V2) | P_relation_rng-{T}(V1,V0)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #514: mergings( V2 == V5, V4 == V7, V3 == V6, V7 == V9; #507 ), references = 1, size of lhs = 6:
% 49.67/49.90 empty-{F}(V0), P_omega-{F}(V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V3,V0), P_powerset-{F}(V4,V3), pppp1-{F}(V0,V3,V5) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #519: mergings( V2 == V6, V4 == V5, V3 == V7, V5 == V8; #508 ), references = 1, size of lhs = 6:
% 49.67/49.90 empty-{F}(V0), P_relation_rng-{F}(V1,V0), P_omega-{F}(V2), P_empty_set-{F}(V3), V1 == V3, pppp1-{F}(V0,V1,V4) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #525: mergings( V2 == V5, V4 == V7, V3 == V6, V7 == V9, V0 == V6; #509 ), references = 1, size of lhs = 6:
% 49.67/49.90 empty-{F}(V0), P_omega-{F}(V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V2,V0), in-{F}(V3,V2), pppp1-{F}(V0,V2,V4) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #533: mergings( V0 == V3, V3 == V5, V4 == V6; #529 ), references = 1, size of lhs = 4:
% 49.67/49.90 pppp0-{F}(V0), empty-{F}(V0), P_omega-{F}(V1), P_empty_set-{F}(V2) | pppp1-{T}(V0,V2,V1)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #555: exists( #179, #153 ), references = 1, size of lhs = 7:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), P_relation_rng-{F}(V2,V3), relation-{F}(V4), P_relation_composition-{F}(V2,V4,V5), P_relation_rng-{F}(V5,V6) | P_relation_image-{T}(V4,V3,V6)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #563: mergings( V3 == V5, V4 == V6; #559 ), references = 1, size of lhs = 4:
% 49.67/49.90 relation-{F}(V0), empty-{F}(V1), P_omega-{F}(V2), P_empty_set-{F}(V3) | P_relation_composition-{T}(V1,V0,V3)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #566: mergings( V3 == V5, V4 == V6; #560 ), references = 1, size of lhs = 5:
% 49.67/49.90 relation-{F}(V0), empty-{F}(V1), P_omega-{F}(V2), P_empty_set-{F}(V3), empty-{F}(V4) | P_relation_composition-{T}(V1,V0,V4)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #571: exists( #176, #166 ), references = 4, size of lhs = 9:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), P_relation_rng-{F}(V2,V3), P_relation_dom-{F}(V2,V4), relation-{F}(V5), P_relation_dom-{F}(V5,V6), subset-{F}(V3,V6), P_relation_composition-{F}(V2,V5,V7) | P_relation_dom-{T}(V7,V4)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #610: exists( #179, #151 ), references = 4, size of lhs = 6:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), P_relation_dom-{F}(V2,V3), P_relation_image-{F}(V2,V4,V5), P_set_intersection2-{F}(V3,V4,V6) | P_relation_image-{T}(V2,V6,V5)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #620: exists( #175, #153 ), references = 5, size of lhs = 7:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), P_relation_rng-{F}(V2,V3), relation-{F}(V4), P_relation_composition-{F}(V2,V4,V5), P_relation_image-{F}(V4,V3,V6) | P_relation_rng-{T}(V5,V6)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #800: mergings( V3 == V5, V5 == V7, V7 == V11, V11 == V16, V9 == V13, V6 == V8, V8 == V12, V12 == V17; #791 ), references = 1, size of lhs = 15:
% 49.67/49.90 empty-{F}(V0), relation-{F}(V0), relation-{F}(V1), P_relation_rng-{F}(V1,V2), P_relation_dom-{F}(V1,V3), relation-{F}(V4), P_relation_image-{F}(V4,V2,V5), P_relation_dom-{F}(V4,V6), subset-{F}(V2,V6), P_omega-{F}(V7), P_empty_set-{F}(V8), P_relation_dom-{F}(V0,V9), subset-{F}(V5,V9), P_relation_dom-{F}(V8,V10), V10 == V3 | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #814: exists( #179, #153 ), references = 1, size of lhs = 7:
% 49.67/49.90 P_omega-{F}(V0), P_empty_set-{F}(V1), relation-{F}(V2), P_relation_rng-{F}(V2,V3), relation-{F}(V4), P_relation_composition-{F}(V2,V4,V5), P_relation_rng-{F}(V5,V6) | P_relation_image-{T}(V4,V3,V6)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #964: mergings( V3 == V4, V4 == V8, V8 == V10, V10 == V15, V15 == V16, V6 == V12, V5 == V9, V9 == V11; #955 ), references = 2, size of lhs = 14:
% 49.67/49.90 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), pppp25-{F}(V8,V9), P_relation_image-{F}(V9,V8,V4) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #974: mergings( V2 == V3, V3 == V5, V5 == V11, V11 == V16, V16 == V17, V9 == V13, V4 == V6, V6 == V12; #965 ), references = 2, size of lhs = 14:
% 49.67/49.90 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), pppp25-{F}(V8,V9), P_relation_image-{F}(V9,V8,V4) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #995: mergings( V3 == V4, V4 == V6, V6 == V11, V11 == V15, V15 == V16, V16 == V18, V18 == V22, V22 == V25, V25 == V26, V8 == V13, V5 == V7, V7 == V12, V12 == V17, V17 == V19, V19 == V23; #979 ), references = 1, size of lhs = 19:
% 49.67/49.90 function-{F}(V0), relation-{F}(V0), function-{F}(V1), relation-{F}(V1), P_relation_dom-{F}(V1,V2), P_relation_dom-{F}(V0,V3), P_relation_rng-{F}(V1,V4), subset-{F}(V4,V3), P_relation_image-{F}(V0,V4,V5), function-{F}(V6), relation-{F}(V6), P_relation_image-{F}(V6,V5,V7), P_empty_set-{F}(V8), P_relation_dom-{F}(V6,V9), subset-{F}(V5,V9), in-{F}(V2,V10), P_omega-{F}(V10), pppp25-{F}(V11,V12), P_relation_image-{F}(V12,V11,V7) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1125: mergings( V4 == V6, V6 == V9; #1121 ), references = 2, size of lhs = 13:
% 49.67/49.90 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}(V0,V5), subset-{F}(V3,V5), P_omega-{F}(V6), pppp1-{F}(V3,V1,V6), pppp25-{F}(V7,V8), P_relation_image-{F}(V8,V7,V4) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1128: mergings( V4 == V6, V6 == V9; #1122 ), references = 2, size of lhs = 13:
% 49.67/49.90 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}(V0,V5), subset-{F}(V3,V5), P_omega-{F}(V6), pppp1-{F}(V3,V1,V6), pppp25-{F}(V7,V8), P_relation_image-{F}(V8,V7,V4) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1210: mergings( V6 == V7, V7 == V8, V5 == V11, V11 == V13, V8 == V10, V10 == V12; #1202 ), references = 1, size of lhs = 11:
% 49.67/49.90 function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), P_omega-{F}(V3), subset-{F}(V4,V2), P_relation_rng-{F}(V5,V4), pppp1-{F}(V4,V5,V3), P_relation_image-{F}(V0,V4,V6), pppp25-{F}(V7,V8), P_relation_image-{F}(V8,V7,V6) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1217: mergings( V6 == V7, V7 == V8, V5 == V11, V11 == V13, V8 == V10, V10 == V12; #1203 ), references = 1, size of lhs = 11:
% 49.67/49.90 function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), P_omega-{F}(V3), subset-{F}(V4,V2), P_relation_rng-{F}(V5,V4), pppp1-{F}(V4,V5,V3), P_relation_image-{F}(V0,V4,V6), pppp25-{F}(V7,V8), P_relation_image-{F}(V8,V7,V6) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1222: exists( #25, #1218 ), references = 2, size of lhs = 10:
% 49.67/49.90 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_relation_image-{F}(V1,V0,V5), pppp25-{F}(V6,V7), P_relation_image-{F}(V7,V6,V5) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1223: exists( #25, #1219 ), references = 1, size of lhs = 10:
% 49.67/49.90 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_relation_image-{F}(V1,V0,V5), pppp25-{F}(V6,V7), P_relation_image-{F}(V7,V6,V5) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1231: mergings( V3 == V9, V6 == V8, V4 == V7; #1226 ), references = 3, size of lhs = 9:
% 49.67/49.90 pppp0-{F}(V0), function-{F}(V1), relation-{F}(V1), pppp25-{F}(V2,V1), P_empty_set-{F}(V3), P_relation_dom-{F}(V1,V4), P_set_intersection2-{F}(V4,V2,V0), subset-{F}(V0,V4), P_omega-{F}(V5) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1235: mergings( V3 == V9, V6 == V8, V4 == V7; #1227 ), references = 2, size of lhs = 9:
% 49.67/49.90 pppp0-{F}(V0), function-{F}(V1), relation-{F}(V1), pppp25-{F}(V2,V1), P_empty_set-{F}(V3), P_relation_dom-{F}(V1,V4), P_set_intersection2-{F}(V4,V2,V0), subset-{F}(V0,V4), P_omega-{F}(V5) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1253: mergings( V3 == V4, V4 == V6, V6 == V7, V7 == V10, V5 == V9; #1246 ), references = 1, size of lhs = 7:
% 49.67/49.90 finite-{F}(V0), function-{F}(V1), relation-{F}(V1), P_relation_dom-{F}(V1,V0), pppp25-{F}(V2,V1), P_empty_set-{F}(V3), P_omega-{F}(V4) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1261: mergings( V2 == V3, V3 == V5, V5 == V7, V7 == V9, V4 == V8; #1254 ), references = 1, size of lhs = 7:
% 49.67/49.90 pppp26-{F}(V0), function-{F}(V0), relation-{F}(V0), finite-{F}(V1), P_relation_dom-{F}(V0,V1), P_empty_set-{F}(V2), P_omega-{F}(V3) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1303: mergings( V3 == V4, V4 == V8, V8 == V10, V5 == V9, V9 == V11; #1297 ), references = 1, size of lhs = 7:
% 49.67/49.90 relation-{F}(V0), P_relation_rng-{F}(V0,V1), relation-{F}(V2), P_relation_image-{F}(V2,V1,V3), empty-{F}(V3), P_omega-{F}(V4), P_empty_set-{F}(V5) | P_relation_composition-{T}(V0,V2,V5)
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1359: mergings( V3 == V4, V4 == V10, V5 == V0, V6 == V1; #1352 ), references = 1, size of lhs = 9:
% 49.67/49.90 function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), P_omega-{F}(V3), pppp25-{F}(V4,V0), P_set_intersection2-{F}(V2,V4,V5), subset-{F}(V5,V2), P_set_intersection2-{F}(V6,V4,V5) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1364: mergings( V3 == V4, V4 == V10, V5 == V0, V6 == V1; #1353 ), references = 1, size of lhs = 9:
% 49.67/49.90 function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), P_omega-{F}(V3), pppp25-{F}(V4,V0), P_set_intersection2-{F}(V2,V4,V5), subset-{F}(V5,V2), P_set_intersection2-{F}(V6,V4,V5) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1370: mergings( V3 == V5, V5 == V6, V6 == V10, V7 == V9, V4 == V8; #1354 ), references = 1, size of lhs = 9:
% 49.67/49.90 function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), P_omega-{F}(V3), pppp25-{F}(V4,V0), P_set_intersection2-{F}(V2,V4,V5), subset-{F}(V5,V2), P_set_intersection2-{F}(V6,V4,V5) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1382: mergings( V3 == V5, V5 == V6, V6 == V9, V4 == V8, V7 == V10; #1374 ), references = 1, size of lhs = 6:
% 49.67/49.90 function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), P_omega-{F}(V3), pppp25-{F}(V4,V0) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1390: mergings( V2 == V4, V4 == V5, V5 == V8, V3 == V6; #1383 ), references = 1, size of lhs = 6:
% 49.67/49.90 pppp26-{F}(V0), function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2), P_omega-{F}(V3) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1398: mergings( V2 == V4, V4 == V5, V5 == V7, V3 == V6; #1391 ), references = 1, size of lhs = 5:
% 49.67/49.90 pppp26-{F}(V0), function-{F}(V0), relation-{F}(V0), P_empty_set-{F}(V1), P_omega-{F}(V2) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1414: mergings( V0 == V3, V3 == V5, V5 == V6, V6 == V8, V1 == V4, V4 == V7; #1405 ), references = 1, size of lhs = 2:
% 49.67/49.90 P_empty_set-{F}(V0), P_omega-{F}(V1) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1422: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5; #1415 ), references = 1, size of lhs = 1:
% 49.67/49.90 P_omega-{F}(V0) | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 #1426: exists( #173, #1415 ), references = 1, size of lhs = 0:
% 49.67/49.90 FALSE | FALSE
% 49.67/49.90 (used 0 times, uses = {})
% 49.67/49.90
% 49.67/49.90 number of learnt formulas = 68
% 49.67/49.90
% 49.67/49.90
% 49.67/49.90 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.67/49.90
% 49.67/49.90 randbase = 1
%------------------------------------------------------------------------------