TSTP Solution File: NUM387+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : NUM387+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n014.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 06:12:22 EDT 2022
% Result : Theorem 0.18s 0.44s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM387+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jul 22 23:12:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 GeoParameters:
% 0.18/0.44
% 0.18/0.44 tptp_input = 1
% 0.18/0.44 tptp_output = 0
% 0.18/0.44 nonempty = 1
% 0.18/0.44 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 0.18/0.44
% 0.18/0.44
% 0.18/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44
% 0.18/0.44 RuleSystem INPUT:
% 0.18/0.44
% 0.18/0.44 Initial Rules:
% 0.18/0.44 #0: input, references = 4, size of lhs = 2:
% 0.18/0.44 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #1: input, references = 3, size of lhs = 1:
% 0.18/0.44 empty-{F}(V0) | function-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #2: input, references = 3, size of lhs = 1:
% 0.18/0.44 empty-{F}(V0) | relation-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #3: input, references = 3, size of lhs = 3:
% 0.18/0.44 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #4: input, references = 3, size of lhs = 3:
% 0.18/0.44 P_set_union2-{F}(V0,V1,V2), P_set_union2-{F}(V1,V0,V3), V2 == V3 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #5: input, references = 4, size of lhs = 4:
% 0.18/0.44 P_succ-{F}(V0,V1), P_singleton-{F}(V0,V2), P_set_union2-{F}(V0,V2,V3), V1 == V3 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #6: input, references = 3, size of lhs = 1:
% 0.18/0.44 #-{F} V0 | EXISTS V1: pppp0-{T}(V0,V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #7: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp0-{F}(V0,V1) | element-{T}(V1,V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #8: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | empty-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #9: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | relation-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #10: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #11: input, references = 3, size of lhs = 3:
% 0.18/0.44 P_empty_set-{F}(V0), P_succ-{F}(V1,V2), empty-{F}(V2) | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #12: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | empty-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #13: input, references = 3, size of lhs = 4:
% 0.18/0.44 P_empty_set-{F}(V0), relation-{F}(V1), P_set_union2-{F}(V2,V1,V3), relation-{F}(V2) | relation-{T}(V3)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #14: input, references = 3, size of lhs = 3:
% 0.18/0.44 P_empty_set-{F}(V0), P_set_union2-{F}(V1,V2,V3), empty-{F}(V3) | empty-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #15: input, references = 3, size of lhs = 3:
% 0.18/0.44 P_empty_set-{F}(V0), P_set_union2-{F}(V2,V1,V3), empty-{F}(V3) | empty-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #16: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | empty-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #17: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | relation-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #18: input, references = 4, size of lhs = 3:
% 0.18/0.44 P_empty_set-{F}(V0), P_set_union2-{F}(V1,V1,V2), V2 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #19: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | EXISTS V1: pppp1-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #20: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp1-{F}(V0) | function-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #21: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp1-{F}(V0) | relation-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #22: input, references = 4, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | EXISTS V1: pppp2-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #23: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp2-{F}(V0) | relation-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #24: input, references = 4, size of lhs = 1:
% 0.18/0.44 pppp2-{F}(V0) | empty-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #25: input, references = 4, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | EXISTS V1: pppp3-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #26: input, references = 5, size of lhs = 1:
% 0.18/0.44 pppp3-{F}(V0) | empty-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #27: input, references = 4, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | EXISTS V1: pppp4-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #28: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp4-{F}(V0) | function-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #29: input, references = 4, size of lhs = 1:
% 0.18/0.44 pppp4-{F}(V0) | empty-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #30: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp4-{F}(V0) | relation-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #31: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | EXISTS V1: pppp5-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #32: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp5-{F}(V0) | relation-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #33: input, references = 3, size of lhs = 2:
% 0.18/0.44 pppp5-{F}(V0), empty-{F}(V0) | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #34: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | EXISTS V1: pppp6-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #35: input, references = 3, size of lhs = 2:
% 0.18/0.44 pppp6-{F}(V0), empty-{F}(V0) | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #36: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | EXISTS V1: pppp7-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #37: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp7-{F}(V0) | one_to_one-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #38: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp7-{F}(V0) | function-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #39: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp7-{F}(V0) | relation-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #40: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | EXISTS V1: pppp8-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #41: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp8-{F}(V0) | relation_empty_yielding-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #42: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp8-{F}(V0) | relation-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #43: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | EXISTS V1: pppp9-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #44: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp9-{F}(V0) | function-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #45: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp9-{F}(V0) | relation_empty_yielding-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #46: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp9-{F}(V0) | relation-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #47: input, references = 3, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | EXISTS V1: pppp10-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #48: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp10-{F}(V0) | function-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #49: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp10-{F}(V0) | relation_non_empty-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #50: input, references = 3, size of lhs = 1:
% 0.18/0.44 pppp10-{F}(V0) | relation-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #51: input, references = 4, size of lhs = 2:
% 0.18/0.44 P_empty_set-{F}(V0), P_succ-{F}(V1,V2) | in-{T}(V1,V2)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #52: input, references = 4, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | EXISTS V1: pppp11-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #53: input, references = 4, size of lhs = 3:
% 0.18/0.44 pppp11-{F}(V0), P_succ-{F}(V0,V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #54: input, references = 4, size of lhs = 3:
% 0.18/0.44 P_empty_set-{F}(V0), P_set_union2-{F}(V1,V0,V2), V2 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #55: input, references = 3, size of lhs = 2:
% 0.18/0.44 P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #56: input, references = 3, size of lhs = 2:
% 0.18/0.44 P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #57: input, references = 6, size of lhs = 3:
% 0.18/0.44 P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #58: input, references = 3, size of lhs = 3:
% 0.18/0.44 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #59: input, references = 4, size of lhs = 4:
% 0.18/0.44 P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #60: input, references = 5, size of lhs = 2:
% 0.18/0.44 #-{F} V0, #-{F} V1 | EXISTS V2: P_set_union2-{T}(V0,V1,V2)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #61: input, references = 4, size of lhs = 1:
% 0.18/0.44 #-{F} V0 | EXISTS V1: P_succ-{T}(V0,V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #62: input, references = 3, size of lhs = 1:
% 0.18/0.44 #-{F} V0 | EXISTS V1: P_singleton-{T}(V0,V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #63: input, references = 4, size of lhs = 0:
% 0.18/0.44 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 number of initial rules = 64
% 0.18/0.44
% 0.18/0.44 Simplifiers:
% 0.18/0.44 #64: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 relation_non_empty-{F}(V0), relation_non_empty-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #65: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 P_set_union2-{F}(V0,V1,V2), P_set_union2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #66: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 P_succ-{F}(V0,V1), P_succ-{F}(V0,V3), V1 == V3 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #67: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 P_singleton-{F}(V0,V1), P_singleton-{F}(V0,V3), V1 == V3 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #68: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #69: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp0-{F}(V0,V1), pppp0-{F}(V0,V3), V1 == V3 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #70: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp1-{F}(V0), pppp1-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #71: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp2-{F}(V0), pppp2-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #72: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp3-{F}(V0), pppp3-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #73: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp4-{F}(V0), pppp4-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #74: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #75: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #76: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp7-{F}(V0), pppp7-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #77: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #78: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #79: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp10-{F}(V0), pppp10-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #80: unsound, references = 3, size of lhs = 3:
% 0.18/0.44 pppp11-{F}(V0), pppp11-{F}(V1), V0 == V1 | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 number of simplifiers = 17
% 0.18/0.44
% 0.18/0.44 Learnt:
% 0.18/0.44 #83: exists( #60, #18 ), references = 1, size of lhs = 2:
% 0.18/0.44 P_empty_set-{F}(V0), #-{F} V1 | P_set_union2-{T}(V1,V1,V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #89: mergings( V0 == V2; #87 ), references = 1, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | pppp2-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #95: mergings( V0 == V2; #92 ), references = 1, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | pppp3-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #97: mergings( V0 == V2; #93 ), references = 1, size of lhs = 2:
% 0.18/0.44 P_empty_set-{F}(V0), empty-{F}(V1) | pppp3-{T}(V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #100: exists( #60, #54 ), references = 1, size of lhs = 2:
% 0.18/0.44 P_empty_set-{F}(V0), #-{F} V1 | P_set_union2-{T}(V1,V0,V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #101: exists( #60, #5 ), references = 1, size of lhs = 2:
% 0.18/0.44 P_succ-{F}(V0,V1), P_singleton-{F}(V0,V2) | P_set_union2-{T}(V0,V2,V1)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #107: mergings( V0 == V2; #105 ), references = 1, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | pppp4-{T}(V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #110: exists( #61, #53 ), references = 2, size of lhs = 1:
% 0.18/0.44 pppp11-{F}(V0) | P_succ-{T}(V0,V0)
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #116: mergings( V0 == V2; #114 ), references = 1, size of lhs = 1:
% 0.18/0.44 P_empty_set-{F}(V0) | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 #118: exists( #63, #114 ), references = 1, size of lhs = 0:
% 0.18/0.44 FALSE | FALSE
% 0.18/0.44 (used 0 times, uses = {})
% 0.18/0.44
% 0.18/0.44 number of learnt formulas = 10
% 0.18/0.44
% 0.18/0.44
% 0.18/0.44 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44
% 0.18/0.44 randbase = 1
%------------------------------------------------------------------------------