%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SEU220+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 06:17:31 EDT 2022
% Result : Theorem 3.72s 3.94s
% Output : Refutation 3.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU220+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jul 22 19:16:36 EDT 2022
% 0.18/0.33 % CPUTime :
% 3.72/3.94 GeoParameters:
% 3.72/3.94
% 3.72/3.94 tptp_input = 1
% 3.72/3.94 tptp_output = 0
% 3.72/3.94 nonempty = 1
% 3.72/3.94 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.72/3.94 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 3.72/3.94
% 3.72/3.94
% 3.72/3.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.72/3.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.72/3.94
% 3.72/3.94 RuleSystem INPUT:
% 3.72/3.94
% 3.72/3.94 Initial Rules:
% 3.72/3.94 #0: input, references = 6, size of lhs = 2:
% 3.72/3.94 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #1: input, references = 3, size of lhs = 1:
% 3.72/3.94 empty-{F}(V0) | function-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #2: input, references = 3, size of lhs = 1:
% 3.72/3.94 empty-{F}(V0) | relation-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #3: input, references = 3, size of lhs = 3:
% 3.72/3.94 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #4: input, references = 4, size of lhs = 3:
% 3.72/3.94 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | relation-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #5: input, references = 4, size of lhs = 3:
% 3.72/3.94 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | function-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #6: input, references = 3, size of lhs = 3:
% 3.72/3.94 relation-{F}(V0), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V1) | relation-{T}(V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #7: input, references = 3, size of lhs = 1:
% 3.72/3.94 #-{F} V0 | EXISTS V1: pppp1-{T}(V0,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #8: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp1-{F}(V0,V1) | element-{T}(V1,V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #9: input, references = 5, size of lhs = 3:
% 3.72/3.94 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #10: input, references = 3, size of lhs = 3:
% 3.72/3.94 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #11: input, references = 3, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | empty-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #12: input, references = 3, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | relation-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #13: input, references = 3, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #14: input, references = 3, size of lhs = 6:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V2,V1,V3), relation-{F}(V2), function-{F}(V2) | relation-{T}(V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #15: input, references = 3, size of lhs = 6:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V2,V1,V3), relation-{F}(V2), function-{F}(V2) | function-{T}(V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #16: input, references = 3, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | empty-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #17: input, references = 3, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | empty-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #18: input, references = 3, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | relation-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #19: input, references = 3, size of lhs = 4:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #20: input, references = 3, size of lhs = 4:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #21: input, references = 5, size of lhs = 3:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #22: input, references = 3, size of lhs = 3:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #23: input, references = 5, size of lhs = 3:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #24: input, references = 3, size of lhs = 3:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #25: input, references = 5, size of lhs = 4:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | empty-{T}(V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #26: input, references = 3, size of lhs = 4:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | relation-{T}(V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #27: input, references = 3, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | EXISTS V1: pppp2-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #28: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp2-{F}(V0) | function-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #29: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp2-{F}(V0) | relation-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #30: input, references = 4, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | EXISTS V1: pppp3-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #31: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp3-{F}(V0) | relation-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #32: input, references = 5, size of lhs = 1:
% 3.72/3.94 pppp3-{F}(V0) | empty-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #33: input, references = 4, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | EXISTS V1: pppp4-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #34: input, references = 5, size of lhs = 1:
% 3.72/3.94 pppp4-{F}(V0) | empty-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #35: input, references = 4, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | EXISTS V1: pppp5-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #36: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp5-{F}(V0) | function-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #37: input, references = 5, size of lhs = 1:
% 3.72/3.94 pppp5-{F}(V0) | empty-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #38: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp5-{F}(V0) | relation-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #39: input, references = 3, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | EXISTS V1: pppp6-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #40: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp6-{F}(V0) | relation-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #41: input, references = 3, size of lhs = 2:
% 3.72/3.94 pppp6-{F}(V0), empty-{F}(V0) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #42: input, references = 3, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | EXISTS V1: pppp7-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #43: input, references = 3, size of lhs = 2:
% 3.72/3.94 pppp7-{F}(V0), empty-{F}(V0) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #44: input, references = 3, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | EXISTS V1: pppp8-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #45: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp8-{F}(V0) | one_to_one-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #46: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp8-{F}(V0) | function-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #47: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp8-{F}(V0) | relation-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #48: input, references = 3, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | EXISTS V1: pppp9-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #49: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp9-{F}(V0) | relation_empty_yielding-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #50: input, references = 3, size of lhs = 1:
% 3.72/3.94 pppp9-{F}(V0) | relation-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #51: input, references = 3, size of lhs = 2:
% 3.72/3.94 P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #52: input, references = 11, size of lhs = 12:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V3,V4), relation-{F}(V3), function-{F}(V3), P_apply-{F}(V4,V5,V6), P_apply-{F}(V1,V5,V7), P_apply-{F}(V3,V7,V8), in-{F}(V5,V2), V6 == V8 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #53: input, references = 4, size of lhs = 2:
% 3.72/3.94 P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #54: input, references = 5, size of lhs = 7:
% 3.72/3.94 P_empty_set-{F}(V0), P_function_inverse-{F}(V1,V2), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), relation-{F}(V2), function-{F}(V2) | pppp0-{T}(V1,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #55: input, references = 3, size of lhs = 9:
% 3.72/3.94 P_empty_set-{F}(V0), P_function_inverse-{F}(V1,V2), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V1,V3), V3 == V2 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #56: input, references = 8, size of lhs = 5:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_dom-{F}(V2,V3), P_relation_rng-{F}(V1,V4), P_relation_dom-{F}(V1,V5), pppp0-{F}(V1,V2) | pppp10-{T}(V1,V2,V3,V4,V5)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #57: input, references = 8, size of lhs = 4:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_dom-{F}(V2,V4), P_relation_rng-{F}(V1,V4), P_relation_dom-{F}(V1,V5) | pppp0-{T}(V1,V2), pppp16-{T}(V1,V2,V4,V5)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #58: input, references = 4, size of lhs = 1:
% 3.72/3.94 pppp16-{F}(V0,V1,V2,V3) | EXISTS V4: pppp13-{T}(V0,V1,V2,V3,V4)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #59: input, references = 4, size of lhs = 1:
% 3.72/3.94 pppp13-{F}(V0,V1,V2,V3,V4) | EXISTS V5: pppp12-{T}(V0,V1,V4,V5,V2,V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #60: input, references = 4, size of lhs = 4:
% 3.72/3.94 pppp12-{F}(V0,V1,V2,V6,V4,V5), P_apply-{F}(V1,V2,V6), P_apply-{F}(V0,V6,V7), in-{F}(V2,V4) | pppp11-{T}(V2,V6,V4,V5,V6,V7)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #61: input, references = 8, size of lhs = 4:
% 3.72/3.94 pppp12-{F}(V0,V1,V2,V3,V4,V5), P_apply-{F}(V1,V2,V6), P_apply-{F}(V0,V3,V7), V2 == V7 | pppp11-{T}(V2,V3,V4,V5,V6,V7)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #62: input, references = 9, size of lhs = 3:
% 3.72/3.94 pppp12-{F}(V0,V1,V2,V3,V4,V5), P_apply-{F}(V1,V2,V6), P_apply-{F}(V0,V3,V7) | pppp11-{T}(V2,V3,V4,V5,V6,V7), in-{T}(V3,V5)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #63: input, references = 6, size of lhs = 2:
% 3.72/3.94 pppp11-{F}(V5,V1,V2,V3,V4,V5), in-{F}(V1,V3) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #64: input, references = 6, size of lhs = 2:
% 3.72/3.94 pppp11-{F}(V0,V1,V2,V3,V4,V5), V1 == V4 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #65: input, references = 13, size of lhs = 1:
% 3.72/3.94 pppp11-{F}(V0,V1,V2,V3,V4,V5) | in-{T}(V0,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #66: input, references = 5, size of lhs = 5:
% 3.72/3.94 pppp10-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V1,V8,V7), P_apply-{F}(V0,V6,V8), in-{F}(V6,V4), V6 == V7 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #67: input, references = 9, size of lhs = 4:
% 3.72/3.94 pppp10-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V1,V8,V7), P_apply-{F}(V0,V6,V8), in-{F}(V6,V4) | in-{T}(V8,V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #68: input, references = 9, size of lhs = 5:
% 3.72/3.94 pppp10-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V1,V5,V7), P_apply-{F}(V0,V7,V8), in-{F}(V5,V3), V5 == V8 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #69: input, references = 5, size of lhs = 4:
% 3.72/3.94 pppp10-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V1,V5,V7), P_apply-{F}(V0,V7,V8), in-{F}(V5,V3) | in-{T}(V7,V4)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #70: input, references = 3, size of lhs = 2:
% 3.72/3.94 pppp10-{F}(V0,V1,V2,V3,V4), V2 == V3 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #71: input, references = 6, size of lhs = 10:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_dom-{F}(V3,V4), P_relation_dom-{F}(V1,V5), P_relation_rng-{F}(V3,V6), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), V2 == V4 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #72: input, references = 6, size of lhs = 10:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_dom-{F}(V3,V4), P_relation_dom-{F}(V1,V5), P_relation_rng-{F}(V3,V6), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), V5 == V6 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #73: input, references = 4, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | EXISTS V1: pppp15-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #74: input, references = 4, size of lhs = 4:
% 3.72/3.94 pppp15-{F}(V0), P_relation_rng-{F}(V0,V1), P_function_inverse-{F}(V0,V2), P_relation_composition-{F}(V2,V0,V3) | EXISTS V4: pppp14-{T}(V4,V0,V1,V2,V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #75: input, references = 7, size of lhs = 4:
% 3.72/3.94 pppp15-{F}(V0), P_relation_rng-{F}(V0,V1), P_function_inverse-{F}(V0,V2), P_relation_composition-{F}(V2,V0,V3) | one_to_one-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #76: input, references = 4, size of lhs = 4:
% 3.72/3.94 pppp15-{F}(V0), P_relation_rng-{F}(V0,V1), P_function_inverse-{F}(V0,V2), P_relation_composition-{F}(V2,V0,V3) | function-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #77: input, references = 4, size of lhs = 4:
% 3.72/3.94 pppp15-{F}(V0), P_relation_rng-{F}(V0,V1), P_function_inverse-{F}(V0,V2), P_relation_composition-{F}(V2,V0,V3) | relation-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #78: input, references = 4, size of lhs = 4:
% 3.72/3.94 pppp14-{F}(V7,V1,V2,V3,V4), P_apply-{F}(V3,V7,V5), P_apply-{F}(V1,V5,V7), P_apply-{F}(V4,V7,V7) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #79: input, references = 7, size of lhs = 4:
% 3.72/3.94 pppp14-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V3,V0,V5), P_apply-{F}(V1,V5,V6), P_apply-{F}(V4,V0,V7) | in-{T}(V0,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #80: input, references = 10, size of lhs = 3:
% 3.72/3.94 P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #81: input, references = 3, size of lhs = 3:
% 3.72/3.94 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #82: input, references = 10, size of lhs = 4:
% 3.72/3.94 P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #83: input, references = 6, size of lhs = 1:
% 3.72/3.94 #-{F} V0 | EXISTS V1: P_function_inverse-{T}(V0,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #84: input, references = 13, size of lhs = 2:
% 3.72/3.94 #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_composition-{T}(V0,V1,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #85: input, references = 4, size of lhs = 0:
% 3.72/3.94 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #86: input, references = 10, size of lhs = 1:
% 3.72/3.94 #-{F} V0 | EXISTS V1: P_relation_dom-{T}(V0,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #87: input, references = 13, size of lhs = 1:
% 3.72/3.94 #-{F} V0 | EXISTS V1: P_relation_rng-{T}(V0,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #88: input, references = 24, size of lhs = 2:
% 3.72/3.94 #-{F} V0, #-{F} V1 | EXISTS V2: P_apply-{T}(V0,V1,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 number of initial rules = 89
% 3.72/3.94
% 3.72/3.94 Simplifiers:
% 3.72/3.94 #89: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 P_function_inverse-{F}(V0,V1), P_function_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #90: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 P_relation_composition-{F}(V0,V1,V2), P_relation_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #91: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #92: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V0,V3), V1 == V3 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #93: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 P_relation_rng-{F}(V0,V1), P_relation_rng-{F}(V0,V3), V1 == V3 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #94: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #95: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp1-{F}(V0,V1), pppp1-{F}(V0,V3), V1 == V3 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #96: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp2-{F}(V0), pppp2-{F}(V1), V0 == V1 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #97: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp3-{F}(V0), pppp3-{F}(V1), V0 == V1 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #98: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp4-{F}(V0), pppp4-{F}(V1), V0 == V1 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #99: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #100: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #101: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp7-{F}(V0), pppp7-{F}(V1), V0 == V1 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #102: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #103: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #104: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V5,V1,V7,V8,V9), V2 == V7 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #105: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V3 == V8 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #106: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #107: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp12-{F}(V0,V1,V2,V3,V4,V5), pppp12-{F}(V0,V1,V2,V9,V4,V5), V3 == V9 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #108: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp12-{F}(V0,V1,V2,V3,V4,V5), pppp12-{F}(V0,V1,V8,V9,V4,V5), V2 == V8 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #109: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp12-{F}(V0,V1,V2,V3,V4,V5), pppp12-{F}(V6,V1,V8,V9,V10,V11), V4 == V10 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #110: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp12-{F}(V0,V1,V2,V3,V4,V5), pppp12-{F}(V0,V7,V8,V9,V10,V11), V4 == V10 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #111: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp12-{F}(V0,V1,V2,V3,V4,V5), pppp12-{F}(V0,V7,V8,V9,V10,V11), V5 == V11 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #112: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp13-{F}(V0,V1,V2,V3,V4), pppp13-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #113: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp13-{F}(V0,V1,V2,V3,V4), pppp13-{F}(V5,V1,V7,V8,V9), V2 == V7 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #114: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp13-{F}(V0,V1,V2,V3,V4), pppp13-{F}(V0,V6,V7,V8,V9), V2 == V7 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #115: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp13-{F}(V0,V1,V2,V3,V4), pppp13-{F}(V0,V6,V7,V8,V9), V3 == V8 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #116: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp14-{F}(V0,V1,V2,V3,V4), pppp14-{F}(V5,V1,V2,V3,V4), V0 == V5 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #117: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp14-{F}(V0,V1,V2,V3,V4), pppp14-{F}(V5,V6,V7,V8,V9), V1 == V6 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #118: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp14-{F}(V0,V1,V2,V3,V4), pppp14-{F}(V5,V1,V7,V8,V9), V2 == V7 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #119: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp14-{F}(V0,V1,V2,V3,V4), pppp14-{F}(V5,V1,V7,V8,V9), V3 == V8 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #120: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp14-{F}(V0,V1,V2,V3,V4), pppp14-{F}(V5,V1,V7,V3,V9), V4 == V9 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #121: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp15-{F}(V0), pppp15-{F}(V1), V0 == V1 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #122: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V4,V1,V6,V7), V2 == V6 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #123: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #124: unsound, references = 3, size of lhs = 3:
% 3.72/3.94 pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V5,V6,V7), V3 == V7 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 number of simplifiers = 36
% 3.72/3.94
% 3.72/3.94 Learnt:
% 3.72/3.94 #130: mergings( V0 == V2; #127 ), references = 1, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | pppp3-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #132: mergings( V0 == V2; #128 ), references = 1, size of lhs = 2:
% 3.72/3.94 P_empty_set-{F}(V0), empty-{F}(V1) | pppp3-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #138: mergings( V0 == V2; #135 ), references = 1, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | pppp4-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #140: mergings( V0 == V2; #136 ), references = 1, size of lhs = 2:
% 3.72/3.94 P_empty_set-{F}(V0), empty-{F}(V1) | pppp4-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #153: mergings( V2 == V3; #150 ), references = 1, size of lhs = 2:
% 3.72/3.94 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_rng-{T}(V0,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #155: mergings( V2 == V3; #151 ), references = 1, size of lhs = 3:
% 3.72/3.94 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_rng-{T}(V0,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #161: mergings( V0 == V2; #158 ), references = 1, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | pppp5-{T}(V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #163: mergings( V0 == V2; #159 ), references = 1, size of lhs = 2:
% 3.72/3.94 P_empty_set-{F}(V0), empty-{F}(V1) | pppp5-{T}(V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #170: mergings( V2 == V3; #167 ), references = 1, size of lhs = 2:
% 3.72/3.94 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_dom-{T}(V0,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #172: mergings( V2 == V3; #168 ), references = 1, size of lhs = 3:
% 3.72/3.94 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_dom-{T}(V0,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #185: mergings( V0 == V5; #183 ), references = 2, size of lhs = 11:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V1,V2), P_relation_dom-{F}(V1,V3), P_function_inverse-{F}(V1,V4), relation-{F}(V5), V5 == V4, P_relation_dom-{F}(V5,V2), function-{F}(V5) | pppp16-{T}(V1,V5,V2,V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #191: exists( #84, #186 ), references = 1, size of lhs = 3:
% 3.72/3.94 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V0,V1,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #192: exists( #84, #187 ), references = 1, size of lhs = 4:
% 3.72/3.94 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V0,V1,V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #207: mergings( V0 == V3; #203 ), references = 1, size of lhs = 3:
% 3.72/3.94 P_empty_set-{F}(V0), element-{F}(V1,V2), V2 == V0 | in-{T}(V1,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #210: mergings( V0 == V3, V2 == V3; #204 ), references = 1, size of lhs = 4:
% 3.72/3.94 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, element-{F}(V2,V0) | in-{T}(V2,V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #212: mergings( V2 == V0; #205 ), references = 1, size of lhs = 3:
% 3.72/3.94 P_empty_set-{F}(V0), pppp7-{F}(V0), element-{F}(V1,V0) | in-{T}(V1,V0)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #228: exists( #87, #72 ), references = 1, size of lhs = 8:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_dom-{F}(V3,V4), P_relation_dom-{F}(V1,V5) | P_relation_rng-{T}(V3,V5)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #232: exists( #87, #71 ), references = 4, size of lhs = 9:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_dom-{F}(V3,V4), V2 == V4, P_relation_dom-{F}(V1,V5) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #234: exists( #86, #231 ), references = 1, size of lhs = 7:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_dom-{F}(V1,V4) | P_relation_dom-{T}(V3,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #253: mergings( V3 == V4; #250 ), references = 1, size of lhs = 3:
% 3.72/3.94 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V1,V0,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #255: mergings( V3 == V4; #251 ), references = 1, size of lhs = 4:
% 3.72/3.94 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V1,V0,V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #279: mergings( V2 == V5; #277 ), references = 2, size of lhs = 10:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1), P_function_inverse-{F}(V0,V2), P_relation_composition-{F}(V2,V0,V3), P_relation_dom-{F}(V2,V4), P_relation_dom-{F}(V0,V5), P_relation_rng-{F}(V2,V6), V5 == V6 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #282: mergings( V2 == V5; #280 ), references = 1, size of lhs = 8:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1), P_function_inverse-{F}(V0,V2), P_relation_composition-{F}(V2,V0,V3), P_relation_dom-{F}(V2,V4), P_relation_rng-{F}(V2,V5) | P_relation_dom-{T}(V0,V5)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #300: exists( #87, #232 ), references = 2, size of lhs = 7:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4) | P_relation_rng-{T}(V1,V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #302: mergings( V3 == V4; #298 ), references = 1, size of lhs = 6:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), P_function_inverse-{F}(V1,V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_dom-{F}(V1,V2) | P_relation_rng-{T}(V1,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #311: mergings( V0 == V6, V3 == V5; #307 ), references = 1, size of lhs = 9:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1), P_relation_rng-{F}(V0,V2), P_function_inverse-{F}(V0,V3), P_relation_dom-{F}(V3,V4), V2 == V4, P_relation_dom-{F}(V0,V5) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #314: mergings( V0 == V6, V3 == V5; #308 ), references = 1, size of lhs = 10:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1), P_relation_rng-{F}(V0,V2), P_function_inverse-{F}(V0,V3), P_relation_dom-{F}(V3,V4), V2 == V4, P_relation_dom-{F}(V0,V5), P_relation_rng-{F}(V3,V6) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #320: mergings( V4 == V0, V3 == V6; #316 ), references = 2, size of lhs = 7:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1), P_relation_rng-{F}(V0,V2), P_function_inverse-{F}(V0,V3), P_relation_dom-{F}(V0,V4) | P_relation_dom-{T}(V3,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #326: exists( #88, #52 ), references = 6, size of lhs = 10:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), in-{F}(V5,V2), P_apply-{F}(V4,V5,V6), P_apply-{F}(V1,V5,V7) | P_apply-{T}(V3,V7,V6)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #329: exists( #88, #327 ), references = 7, size of lhs = 12:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), in-{F}(V5,V2), P_apply-{F}(V4,V5,V6), V5 == V6, in-{F}(V5,V7), pppp10-{F}(V3,V1,V8,V7,V9) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #335: exists( #88, #329 ), references = 5, size of lhs = 10:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), in-{F}(V5,V2), in-{F}(V5,V6), pppp10-{F}(V3,V1,V7,V6,V8) | P_apply-{T}(V4,V5,V5)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #351: mergings( V9 == V13; #349 ), references = 1, size of lhs = 13:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), in-{F}(V5,V2), P_apply-{F}(V4,V5,V6), in-{F}(V5,V7), pppp10-{F}(V1,V3,V8,V9,V7), P_apply-{F}(V10,V6,V11), pppp10-{F}(V10,V3,V8,V9,V12) | P_apply-{T}(V1,V5,V11)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #361: mergings( V3 == V7, V7 == V10, V4 == V8, V17 == V23, V19 == V21; #355 ), references = 1, size of lhs = 24:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), in-{F}(V2,V1), in-{F}(V2,V3), relation-{F}(V4), function-{F}(V4), in-{F}(V2,V5), P_empty_set-{F}(V6), relation-{F}(V7), function-{F}(V7), P_relation_dom-{F}(V7,V8), in-{F}(V2,V8), relation-{F}(V9), function-{F}(V9), P_relation_composition-{F}(V7,V9,V0), P_apply-{F}(V7,V2,V10), V2 == V10, P_apply-{F}(V11,V2,V10), in-{F}(V2,V12), pppp10-{F}(V4,V0,V13,V3,V14), pppp10-{F}(V9,V0,V13,V12,V15), pppp10-{F}(V0,V4,V16,V17,V5), pppp10-{F}(V11,V4,V16,V17,V18) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #376: mergings( V0 == V5, V5 == V6, V6 == V7, V7 == V14, V2 == V8, V8 == V9, V9 == V12, V4 == V18, V12 == V17, V20 == V21, V17 == V11, V13 == V22; #363 ), references = 1, size of lhs = 19:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), P_empty_set-{F}(V2), relation-{F}(V3), function-{F}(V3), P_relation_dom-{F}(V3,V4), in-{F}(V5,V4), in-{F}(V5,V1), in-{F}(V5,V6), relation-{F}(V7), function-{F}(V7), P_relation_composition-{F}(V3,V7,V0), P_relation_rng-{F}(V7,V1), P_relation_dom-{F}(V7,V8), P_apply-{F}(V3,V5,V9), V5 == V9, P_apply-{F}(V7,V5,V9), pppp10-{F}(V0,V0,V10,V1,V6) | pppp16-{T}(V7,V0,V1,V8)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #378: exists( #84, #279 ), references = 2, size of lhs = 9:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1), P_function_inverse-{F}(V0,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V0,V4), P_relation_rng-{F}(V2,V5), V4 == V5 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #390: exists( #88, #388 ), references = 1, size of lhs = 3:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), pppp12-{F}(V0,V3,V4,V1,V5,V6), V4 == V2 | P_apply-{T}(V3,V4,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #397: disj( #62, input ), references = 3, size of lhs = 4:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), P_apply-{F}(V3,V4,V5), V4 == V2, pppp12-{F}(V3,V0,V1,V4,V6,V7) | in-{T}(V4,V7)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #402: exists( #88, #398 ), references = 1, size of lhs = 3:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), pppp12-{F}(V3,V0,V1,V4,V5,V4), V4 == V2 | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #404: exists( #88, #401 ), references = 1, size of lhs = 1:
% 3.72/3.94 pppp12-{F}(V0,V1,V2,V3,V4,V3) | P_apply-{T}(V1,V2,V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #414: exists( #88, #408 ), references = 2, size of lhs = 4:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), P_apply-{F}(V3,V1,V4), pppp12-{F}(V5,V0,V1,V4,V6,V7), pppp10-{F}(V3,V5,V8,V9,V6) | P_apply-{T}(V5,V4,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #415: exists( #88, #409 ), references = 1, size of lhs = 4:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), P_apply-{F}(V3,V1,V4), pppp12-{F}(V5,V0,V1,V4,V6,V7), pppp10-{F}(V5,V3,V8,V6,V9) | P_apply-{T}(V5,V4,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #418: mergings( V3 == V5; #416 ), references = 1, size of lhs = 3:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), pppp12-{F}(V3,V0,V1,V2,V4,V2), P_apply-{F}(V3,V2,V5) | pppp11-{T}(V1,V2,V4,V2,V2,V5)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #438: exists( #88, #436 ), references = 1, size of lhs = 11:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), pppp10-{F}(V3,V1,V5,V2,V6), P_apply-{F}(V7,V8,V9), pppp12-{F}(V4,V7,V8,V10,V11,V2), V10 == V9 | P_apply-{T}(V4,V10,V10)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #444: mergings( V11 == V12, V5 == V13; #441 ), references = 1, size of lhs = 10:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), pppp10-{F}(V3,V1,V5,V2,V6), pppp12-{F}(V4,V7,V8,V9,V10,V2), V8 == V9 | P_apply-{T}(V7,V8,V9)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #448: disj( #62, exists( #88, #327 ) ), references = 1, size of lhs = 13:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), P_apply-{F}(V4,V5,V6), V5 == V6, P_apply-{F}(V7,V5,V8), pppp10-{F}(V3,V1,V9,V2,V10), pppp12-{F}(V7,V11,V12,V5,V13,V2), P_apply-{F}(V11,V12,V14) | pppp11-{T}(V12,V5,V13,V2,V14,V8)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #449: disj( #62, input ), references = 1, size of lhs = 14:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), P_apply-{F}(V4,V5,V6), P_apply-{F}(V1,V5,V7), P_apply-{F}(V3,V7,V8), V6 == V8, P_apply-{F}(V9,V5,V10), pppp12-{F}(V9,V11,V12,V5,V13,V2), P_apply-{F}(V11,V12,V14) | pppp11-{T}(V12,V5,V13,V2,V14,V10)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #481: exists( #88, #479 ), references = 1, size of lhs = 3:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), pppp12-{F}(V3,V0,V1,V4,V5,V6), V4 == V2 | P_apply-{T}(V3,V4,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #487: mergings( V7 == V5, V8 == V6; #484 ), references = 1, size of lhs = 2:
% 3.72/3.94 pppp10-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V1,V0,V5,V6,V7,V3) | P_apply-{T}(V0,V5,V6)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #497: mergings( V8 == V12; #494 ), references = 2, size of lhs = 20:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V0,V2,V3), P_empty_set-{F}(V4), relation-{F}(V5), function-{F}(V5), P_relation_dom-{F}(V5,V1), relation-{F}(V6), P_relation_composition-{F}(V5,V6,V3), function-{F}(V6), P_apply-{F}(V5,V7,V8), P_apply-{F}(V6,V8,V9), V7 == V9, P_apply-{F}(V10,V7,V11), pppp10-{F}(V2,V0,V12,V1,V13), pppp12-{F}(V10,V14,V15,V7,V16,V1), P_apply-{F}(V14,V15,V17) | pppp11-{T}(V15,V7,V16,V1,V17,V11)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #498: disj( #62, #69+#329 ), references = 3, size of lhs = 16:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), pppp10-{F}(V3,V1,V5,V2,V6), P_apply-{F}(V4,V7,V8), V7 == V8, P_apply-{F}(V9,V10,V7), P_apply-{F}(V11,V10,V12), P_apply-{F}(V13,V7,V14), pppp10-{F}(V13,V9,V15,V16,V2), pppp12-{F}(V11,V17,V18,V10,V19,V16), P_apply-{F}(V17,V18,V20) | pppp11-{T}(V18,V10,V19,V16,V20,V12)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #507: mergings( V3 == V8, V8 == V10; #503 ), references = 1, size of lhs = 25:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V0,V2,V3), relation-{F}(V4), function-{F}(V4), P_relation_dom-{F}(V4,V1), relation-{F}(V5), P_relation_composition-{F}(V4,V5,V3), function-{F}(V5), P_empty_set-{F}(V6), relation-{F}(V7), function-{F}(V7), P_relation_dom-{F}(V7,V8), relation-{F}(V9), function-{F}(V9), P_relation_composition-{F}(V7,V9,V5), P_apply-{F}(V4,V10,V11), P_apply-{F}(V12,V10,V13), pppp12-{F}(V12,V14,V11,V10,V8,V1), P_apply-{F}(V14,V11,V15), pppp10-{F}(V2,V0,V16,V1,V17), pppp10-{F}(V9,V7,V18,V8,V19) | P_apply-{T}(V5,V11,V10), P_apply-{T}(V5,V11,V11)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #510: mergings( V3 == V8, V8 == V10; #504 ), references = 1, size of lhs = 26:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V0,V2,V3), relation-{F}(V4), function-{F}(V4), P_relation_dom-{F}(V4,V1), relation-{F}(V5), P_relation_composition-{F}(V4,V5,V3), function-{F}(V5), P_empty_set-{F}(V6), relation-{F}(V7), function-{F}(V7), P_relation_dom-{F}(V7,V8), relation-{F}(V9), function-{F}(V9), P_relation_composition-{F}(V7,V9,V5), P_apply-{F}(V4,V10,V11), P_apply-{F}(V7,V11,V12), P_apply-{F}(V9,V12,V13), P_apply-{F}(V14,V10,V15), pppp12-{F}(V14,V16,V11,V10,V8,V1), P_apply-{F}(V16,V11,V17), pppp10-{F}(V2,V0,V18,V1,V19) | P_apply-{T}(V5,V11,V10), P_apply-{T}(V5,V11,V13)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #521: mergings( V0 == V5, V5 == V8, V8 == V22, V22 == V26; #515 ), references = 1, size of lhs = 46:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V0,V2,V3), relation-{F}(V4), function-{F}(V4), P_relation_dom-{F}(V4,V1), relation-{F}(V5), P_relation_composition-{F}(V4,V5,V3), function-{F}(V5), relation-{F}(V6), function-{F}(V6), P_relation_dom-{F}(V6,V7), relation-{F}(V8), function-{F}(V8), P_relation_composition-{F}(V6,V8,V5), relation-{F}(V9), function-{F}(V9), P_relation_dom-{F}(V9,V10), relation-{F}(V11), function-{F}(V11), P_relation_composition-{F}(V9,V11,V5), P_empty_set-{F}(V12), relation-{F}(V13), function-{F}(V13), P_relation_dom-{F}(V13,V14), relation-{F}(V15), function-{F}(V15), P_relation_composition-{F}(V13,V15,V5), P_apply-{F}(V4,V16,V17), V17 == V16, P_apply-{F}(V18,V16,V19), pppp12-{F}(V18,V20,V17,V16,V7,V1), P_apply-{F}(V20,V17,V21), pppp10-{F}(V2,V0,V22,V1,V23), pppp10-{F}(V8,V6,V24,V7,V25), pppp10-{F}(V11,V9,V26,V10,V27), P_apply-{F}(V28,V17,V29), pppp10-{F}(V15,V13,V30,V14,V31), P_apply-{F}(V32,V33,V17), P_apply-{F}(V34,V33,V35), pppp12-{F}(V34,V28,V17,V33,V14,V36), P_apply-{F}(V37,V17,V38), pppp10-{F}(V37,V32,V39,V36,V10) | P_apply-{T}(V5,V17,V17)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #526: mergings( V0 == V5, V5 == V8, V8 == V22, V22 == V26; #516 ), references = 1, size of lhs = 48:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V0,V2,V3), relation-{F}(V4), function-{F}(V4), P_relation_dom-{F}(V4,V1), relation-{F}(V5), P_relation_composition-{F}(V4,V5,V3), function-{F}(V5), relation-{F}(V6), function-{F}(V6), P_relation_dom-{F}(V6,V7), relation-{F}(V8), function-{F}(V8), P_relation_composition-{F}(V6,V8,V5), relation-{F}(V9), function-{F}(V9), P_relation_dom-{F}(V9,V10), relation-{F}(V11), function-{F}(V11), P_relation_composition-{F}(V9,V11,V5), P_empty_set-{F}(V12), relation-{F}(V13), function-{F}(V13), P_relation_dom-{F}(V13,V14), relation-{F}(V15), function-{F}(V15), P_relation_composition-{F}(V13,V15,V5), P_apply-{F}(V4,V16,V17), V17 == V16, P_apply-{F}(V13,V17,V18), P_apply-{F}(V15,V18,V19), V16 == V19, P_apply-{F}(V20,V16,V21), pppp12-{F}(V20,V22,V17,V16,V7,V1), P_apply-{F}(V22,V17,V23), pppp10-{F}(V2,V0,V24,V1,V25), pppp10-{F}(V8,V6,V26,V7,V27), pppp10-{F}(V11,V9,V28,V10,V29), P_apply-{F}(V30,V17,V31), P_apply-{F}(V32,V33,V17), P_apply-{F}(V34,V33,V35), pppp12-{F}(V34,V30,V17,V33,V14,V36), P_apply-{F}(V37,V17,V38), pppp10-{F}(V37,V32,V39,V36,V10) | P_apply-{T}(V5,V17,V17)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #550: exists( #88, #544 ), references = 1, size of lhs = 21:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V0,V2,V3), P_empty_set-{F}(V4), relation-{F}(V5), function-{F}(V5), P_relation_dom-{F}(V5,V1), relation-{F}(V6), P_relation_composition-{F}(V5,V6,V3), function-{F}(V6), pppp10-{F}(V2,V0,V7,V1,V8), P_apply-{F}(V5,V9,V10), P_apply-{F}(V11,V9,V12), P_apply-{F}(V13,V12,V9), P_apply-{F}(V14,V12,V15), pppp12-{F}(V11,V14,V12,V9,V16,V1), P_apply-{F}(V17,V9,V18), pppp10-{F}(V13,V17,V19,V1,V16) | P_apply-{T}(V6,V10,V9)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #567: disj( #62, input ), references = 1, size of lhs = 14:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), P_apply-{F}(V4,V5,V6), P_apply-{F}(V1,V5,V7), P_apply-{F}(V3,V7,V8), V6 == V8, P_apply-{F}(V9,V5,V10), pppp12-{F}(V9,V11,V12,V5,V13,V2), P_apply-{F}(V11,V12,V14) | pppp11-{T}(V12,V5,V13,V2,V14,V10)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #572: mergings( V3 == V7; #570 ), references = 1, size of lhs = 20:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V0,V2,V3), relation-{F}(V3), function-{F}(V3), P_empty_set-{F}(V4), relation-{F}(V5), function-{F}(V5), P_relation_dom-{F}(V5,V6), P_relation_composition-{F}(V5,V3,V7), P_apply-{F}(V7,V8,V9), P_apply-{F}(V5,V8,V10), P_apply-{F}(V0,V10,V11), P_apply-{F}(V2,V11,V12), P_apply-{F}(V13,V10,V14), pppp12-{F}(V13,V15,V8,V10,V6,V1), P_apply-{F}(V15,V8,V16) | P_apply-{T}(V3,V10,V12), P_apply-{T}(V3,V10,V9)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #599: mergings( V3 == V6; #596 ), references = 1, size of lhs = 6:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), P_apply-{F}(V3,V1,V2), P_apply-{F}(V4,V2,V1), P_apply-{F}(V5,V2,V6), pppp12-{F}(V4,V0,V1,V2,V7,V8), pppp10-{F}(V3,V5,V9,V8,V7) | in-{T}(V2,V8)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #601: mergings( V3 == V6; #597 ), references = 1, size of lhs = 7:
% 3.72/3.94 in-{F}(V0,V1), P_apply-{F}(V2,V3,V1), P_apply-{F}(V4,V3,V5), P_apply-{F}(V6,V1,V7), pppp10-{F}(V2,V6,V8,V0,V9), pppp12-{F}(V10,V4,V3,V5,V9,V11), P_apply-{F}(V10,V5,V12) | in-{T}(V5,V11)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #613: mergings( V6 == V8, V8 == V9, V9 == V10, V7 == V3, V2 == V11; #607 ), references = 1, size of lhs = 2:
% 3.72/3.94 pppp10-{F}(V0,V1,V2,V3,V4), pppp13-{F}(V1,V0,V4,V3,V5) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #620: mergings( V7 == V8, V8 == V5, V5 == V9, V3 == V6, V2 == V10; #614 ), references = 3, size of lhs = 2:
% 3.72/3.94 pppp16-{F}(V0,V1,V2,V3), pppp10-{F}(V1,V0,V4,V3,V2) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #627: mergings( V5 == V6, V6 == V7, V7 == V9, V4 == V8, V2 == V10; #621 ), references = 1, size of lhs = 5:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), P_relation_rng-{F}(V3,V2), P_relation_dom-{F}(V3,V4), pppp10-{F}(V1,V3,V5,V4,V2) | pppp0-{T}(V3,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #634: exists( #88, #629 ), references = 2, size of lhs = 7:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), P_apply-{F}(V3,V2,V4), P_apply-{F}(V5,V1,V6), P_apply-{F}(V7,V6,V8), V1 == V8, pppp14-{F}(V1,V3,V9,V0,V10), pppp10-{F}(V5,V7,V11,V12,V9) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #635: exists( #88, #630 ), references = 2, size of lhs = 7:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), P_apply-{F}(V3,V2,V4), pppp14-{F}(V1,V3,V5,V0,V6), P_apply-{F}(V7,V1,V8), P_apply-{F}(V9,V8,V10), V1 == V10, pppp10-{F}(V9,V7,V11,V5,V12) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #640: exists( #88, #634 ), references = 2, size of lhs = 4:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), P_apply-{F}(V3,V1,V2), pppp14-{F}(V1,V4,V5,V0,V6), pppp10-{F}(V3,V4,V7,V8,V5) | P_apply-{T}(V4,V2,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #641: exists( #88, #635 ), references = 1, size of lhs = 4:
% 3.72/3.94 P_apply-{F}(V0,V1,V2), P_apply-{F}(V3,V1,V2), pppp14-{F}(V1,V4,V5,V0,V6), pppp10-{F}(V4,V3,V7,V5,V8) | P_apply-{T}(V4,V2,V1)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #650: mergings( V4 == V10, V8 == V11; #646 ), references = 2, size of lhs = 12:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), P_apply-{F}(V4,V5,V6), V6 == V5, pppp14-{F}(V5,V3,V2,V1,V7), P_apply-{F}(V7,V5,V8), pppp10-{F}(V1,V3,V9,V10,V2) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #653: mergings( V5 == V14, V10 == V15; #647 ), references = 2, size of lhs = 13:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), P_apply-{F}(V4,V5,V6), V5 == V6, pppp10-{F}(V3,V1,V7,V2,V8), P_apply-{F}(V9,V5,V10), pppp14-{F}(V5,V11,V2,V12,V9), pppp10-{F}(V12,V11,V13,V14,V2) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #656: exists( #88, #650 ), references = 1, size of lhs = 9:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), pppp14-{F}(V5,V3,V2,V1,V4), pppp10-{F}(V1,V3,V6,V7,V2) | P_apply-{T}(V4,V5,V5)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #657: exists( #88, #653 ), references = 1, size of lhs = 10:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), pppp10-{F}(V3,V1,V5,V2,V6), pppp14-{F}(V7,V8,V2,V9,V4), pppp10-{F}(V9,V8,V10,V11,V2) | P_apply-{T}(V4,V7,V7)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #662: mergings( V5 == V6, V3 == V7; #659 ), references = 1, size of lhs = 3:
% 3.72/3.94 P_apply-{F}(V0,V1,V1), pppp14-{F}(V1,V2,V3,V4,V0), pppp10-{F}(V4,V2,V5,V6,V3) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #667: mergings( V6 == V8, V7 == V9; #664 ), references = 1, size of lhs = 11:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_relation_rng-{F}(V0,V1), P_function_inverse-{F}(V0,V2), relation-{F}(V2), function-{F}(V2), P_relation_dom-{F}(V2,V1), P_empty_set-{F}(V3), P_relation_composition-{F}(V2,V0,V4), pppp10-{F}(V2,V0,V5,V6,V1) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #671: mergings( V5 == V7, V6 == V8; #668 ), references = 3, size of lhs = 10:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_relation_rng-{F}(V0,V1), P_function_inverse-{F}(V0,V2), relation-{F}(V2), function-{F}(V2), P_relation_dom-{F}(V2,V1), P_empty_set-{F}(V3), pppp10-{F}(V2,V0,V4,V5,V1) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #678: exists( #87, #378 ), references = 2, size of lhs = 7:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1), P_function_inverse-{F}(V0,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V0,V4) | P_relation_rng-{T}(V2,V4)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #701: mergings( V0 == V5, V4 == V6, V3 == V7; #696 ), references = 2, size of lhs = 11:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_function_inverse-{F}(V0,V1), relation-{F}(V1), function-{F}(V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V0,V3), P_relation_dom-{F}(V0,V4), pppp16-{F}(V1,V0,V4,V3), P_relation_dom-{F}(V1,V5) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #709: mergings( V0 == V7, V2 == V8, V8 == V9, V4 == V10, V10 == V6; #703 ), references = 1, size of lhs = 12:
% 3.72/3.94 one_to_one-{F}(V0), relation-{F}(V0), function-{F}(V0), P_relation_rng-{F}(V0,V1), pppp15-{F}(V2), relation-{F}(V2), function-{F}(V2), P_relation_dom-{F}(V2,V1), P_function_inverse-{F}(V2,V0), P_relation_rng-{F}(V2,V3), P_relation_dom-{F}(V0,V3), P_empty_set-{F}(V4) | P_function_inverse-{T}(V0,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #728: mergings( V4 == V2, V2 == V13, V3 == V7, V7 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V14, V14 == V16, V8 == V5, V5 == V15, V6 == V0; #715 ), references = 1, size of lhs = 9:
% 3.72/3.94 one_to_one-{F}(V0), relation-{F}(V0), function-{F}(V0), pppp15-{F}(V1), relation-{F}(V1), function-{F}(V1), P_function_inverse-{F}(V1,V0), P_relation_dom-{F}(V1,V2), P_empty_set-{F}(V3) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #739: mergings( V3 == V9, V9 == V10, V2 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V11, V11 == V12; #729 ), references = 1, size of lhs = 8:
% 3.72/3.94 one_to_one-{F}(V0), relation-{F}(V0), function-{F}(V0), pppp15-{F}(V1), relation-{F}(V1), function-{F}(V1), P_function_inverse-{F}(V1,V0), P_empty_set-{F}(V2) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #750: mergings( V4 == V6, V2 == V3, V5 == V7; #746 ), references = 1, size of lhs = 7:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_rng-{F}(V2,V4) | P_relation_dom-{T}(V1,V4)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #767: mergings( V0 == V5, V5 == V9, V2 == V6, V7 == V4, V6 == V8; #761 ), references = 1, size of lhs = 11:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), P_relation_rng-{F}(V0,V2), P_function_inverse-{F}(V0,V3), relation-{F}(V3), function-{F}(V3), P_relation_dom-{F}(V3,V2), P_relation_rng-{F}(V3,V1), P_empty_set-{F}(V4) | pppp16-{T}(V3,V0,V1,V2)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #780: mergings( V2 == V6, V6 == V8, V8 == V9, V9 == V10, V10 == V12, V7 == V4, V4 == V11, V5 == V0; #771 ), references = 1, size of lhs = 8:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), pppp15-{F}(V1), relation-{F}(V1), function-{F}(V1), P_function_inverse-{F}(V1,V0), P_relation_dom-{F}(V1,V2), P_empty_set-{F}(V3) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #787: mergings( V2 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #781 ), references = 1, size of lhs = 7:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), pppp15-{F}(V1), relation-{F}(V1), function-{F}(V1), P_function_inverse-{F}(V1,V0), P_empty_set-{F}(V2) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #796: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #790 ), references = 2, size of lhs = 4:
% 3.72/3.94 pppp15-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #807: mergings( V3 == V4; #803 ), references = 2, size of lhs = 4:
% 3.72/3.94 pppp15-{F}(V0), P_relation_rng-{F}(V0,V1), P_function_inverse-{F}(V0,V2), P_empty_set-{F}(V3) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #814: mergings( V0 == V5, V2 == V8, V4 == V7, V8 == V6; #809 ), references = 1, size of lhs = 5:
% 3.72/3.94 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), P_relation_dom-{F}(V1,V3), pppp16-{F}(V4,V1,V3,V2), P_relation_dom-{F}(V4,V2) | pppp16-{T}(V1,V4,V2,V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #830: exists( #87, #232 ), references = 1, size of lhs = 7:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4) | P_relation_rng-{T}(V1,V3)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #837: exists( #88, #52 ), references = 1, size of lhs = 10:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V1,V3,V4), in-{F}(V5,V2), P_apply-{F}(V1,V5,V6), P_apply-{F}(V3,V6,V7) | P_apply-{T}(V4,V5,V7)
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #847: mergings( V3 == V7, V7 == V10, V4 == V8; #843 ), references = 1, size of lhs = 22:
% 3.72/3.94 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), in-{F}(V2,V1), in-{F}(V2,V3), relation-{F}(V4), function-{F}(V4), P_apply-{F}(V0,V2,V5), P_empty_set-{F}(V6), relation-{F}(V7), function-{F}(V7), P_relation_dom-{F}(V7,V8), relation-{F}(V9), function-{F}(V9), P_relation_composition-{F}(V7,V9,V4), P_apply-{F}(V7,V5,V10), P_apply-{F}(V9,V10,V11), V2 == V11, pppp10-{F}(V4,V0,V12,V3,V13), in-{F}(V14,V15), P_apply-{F}(V16,V14,V5), pppp10-{F}(V16,V4,V17,V8,V15) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #858: mergings( V3 == V7, V4 == V8; #855 ), references = 1, size of lhs = 13:
% 3.72/3.94 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V1,V2), in-{F}(V3,V2), in-{F}(V3,V4), relation-{F}(V5), function-{F}(V5), P_apply-{F}(V1,V3,V6), pppp10-{F}(V5,V1,V7,V4,V8), in-{F}(V9,V10), P_apply-{F}(V11,V9,V6), pppp10-{F}(V11,V5,V12,V6,V10) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #865: exists( #87, #807 ), references = 1, size of lhs = 3:
% 3.72/3.94 pppp15-{F}(V0), P_function_inverse-{F}(V0,V1), P_empty_set-{F}(V2) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #867: exists( #83, #864 ), references = 1, size of lhs = 2:
% 3.72/3.94 pppp15-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #870: mergings( V0 == V2; #868 ), references = 1, size of lhs = 1:
% 3.72/3.94 P_empty_set-{F}(V0) | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 #872: exists( #85, #868 ), references = 1, size of lhs = 0:
% 3.72/3.94 FALSE | FALSE
% 3.72/3.94 (used 0 times, uses = {})
% 3.72/3.94
% 3.72/3.94 number of learnt formulas = 93
% 3.72/3.94
% 3.72/3.94
% 3.72/3.94 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.72/3.94
% 3.72/3.94 randbase = 1
%------------------------------------------------------------------------------