TSTP Solution File: SEU010+1 by Geo-III---2018C

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Geo-III---2018C
% Problem  : SEU010+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : geo -tptp_input -nonempty -inputfile %s

% Computer : n016.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 06:17:04 EDT 2022

% Result   : Theorem 0.76s 0.95s
% Output   : Refutation 0.76s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU010+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command  : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33  % Computer : n016.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 19:36:45 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.76/0.95  GeoParameters:
% 0.76/0.95  
% 0.76/0.95  tptp_input =     1
% 0.76/0.95  tptp_output =    0
% 0.76/0.95  nonempty =       1
% 0.76/0.95  inputfile =      /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.76/0.95  includepath =    /export/starexec/sandbox/solver/bin/../../benchmark/
% 0.76/0.95  
% 0.76/0.95  
% 0.76/0.95  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.76/0.95  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.76/0.95  
% 0.76/0.95  RuleSystem INPUT:
% 0.76/0.95  
% 0.76/0.95  Initial Rules:
% 0.76/0.95  #0: input, references = 3, size of lhs = 2:
% 0.76/0.95     in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #1: input, references = 3, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | empty-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #2: input, references = 3, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | relation-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #3: input, references = 3, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | empty-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #4: input, references = 3, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | relation-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #5: input, references = 3, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #6: input, references = 3, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | empty-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #7: input, references = 3, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #8: input, references = 3, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3), in-{F}(V4,V1) | element-{T}(V4,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #9: input, references = 3, size of lhs = 5:
% 0.76/0.95     P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V1), element-{F}(V3,V2), in-{F}(V4,V3) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #10: input, references = 5, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), #-{F} V1 | EXISTS V2: pppp0-{T}(V1,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #11: input, references = 6, size of lhs = 1:
% 0.76/0.95     pppp0-{F}(V0,V1) | element-{T}(V1,V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #12: input, references = 3, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), empty-{F}(V1) | function-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #13: input, references = 3, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V2) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #14: input, references = 3, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #15: input, references = 3, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #16: input, references = 5, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #17: input, references = 3, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #18: input, references = 5, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #19: input, references = 3, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #20: input, references = 4, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | empty-{T}(V3)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #21: input, references = 3, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | relation-{T}(V3)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #22: input, references = 5, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V1,V2,V3), empty-{F}(V2) | empty-{T}(V3)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #23: input, references = 3, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V1,V2,V3), empty-{F}(V2) | relation-{T}(V3)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #24: input, references = 3, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), empty-{F}(V1) | relation-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #25: input, references = 5, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #26: input, references = 11, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #27: input, references = 3, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #28: input, references = 9, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #29: input, references = 5, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), #-{F} V1 | subset-{T}(V1,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #30: input, references = 3, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), relation-{F}(V2) | relation-{T}(V3)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #31: input, references = 4, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), P_identity_relation-{F}(V1,V2) | relation-{T}(V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #32: input, references = 3, size of lhs = 6:
% 0.76/0.95     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)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #33: input, references = 3, size of lhs = 6:
% 0.76/0.95     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)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #34: input, references = 3, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), P_identity_relation-{F}(V1,V2) | relation-{T}(V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #35: input, references = 3, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), P_identity_relation-{F}(V1,V2) | function-{T}(V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #36: input, references = 3, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | EXISTS V1: pppp1-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #37: input, references = 3, size of lhs = 1:
% 0.76/0.95     pppp1-{F}(V0) | function-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #38: input, references = 3, size of lhs = 1:
% 0.76/0.95     pppp1-{F}(V0) | relation-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #39: input, references = 4, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | empty-{T}(V1), pppp10-{T}(V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #40: input, references = 3, size of lhs = 1:
% 0.76/0.95     pppp10-{F}(V0) | EXISTS V1: pppp2-{T}(V1,V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #41: input, references = 3, size of lhs = 2:
% 0.76/0.95     pppp2-{F}(V0,V1), empty-{F}(V0) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #42: input, references = 3, size of lhs = 1:
% 0.76/0.95     pppp2-{F}(V0,V1) | element-{T}(V0,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #43: input, references = 4, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | EXISTS V3: pppp3-{T}(V3,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #44: input, references = 4, size of lhs = 1:
% 0.76/0.95     pppp3-{F}(V0,V1) | empty-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #45: input, references = 3, size of lhs = 1:
% 0.76/0.95     pppp3-{F}(V0,V1) | element-{T}(V0,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #46: input, references = 4, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | EXISTS V1: pppp4-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #47: input, references = 3, size of lhs = 1:
% 0.76/0.95     pppp4-{F}(V0) | relation-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #48: input, references = 5, size of lhs = 1:
% 0.76/0.95     pppp4-{F}(V0) | empty-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #49: input, references = 3, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | EXISTS V1: pppp5-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #50: input, references = 3, size of lhs = 1:
% 0.76/0.95     pppp5-{F}(V0) | relation-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #51: input, references = 3, size of lhs = 2:
% 0.76/0.95     pppp5-{F}(V0), empty-{F}(V0) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #52: input, references = 3, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | EXISTS V1: pppp6-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #53: input, references = 3, size of lhs = 1:
% 0.76/0.95     pppp6-{F}(V0) | relation_empty_yielding-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #54: input, references = 3, size of lhs = 1:
% 0.76/0.95     pppp6-{F}(V0) | relation-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #55: input, references = 4, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | EXISTS V1: pppp7-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #56: input, references = 5, size of lhs = 1:
% 0.76/0.95     pppp7-{F}(V0) | empty-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #57: input, references = 3, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | EXISTS V1: pppp8-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #58: input, references = 3, size of lhs = 2:
% 0.76/0.95     pppp8-{F}(V0), empty-{F}(V0) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #59: input, references = 3, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3) | subset-{T}(V1,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #60: input, references = 3, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), subset-{F}(V1,V2) | element-{T}(V1,V3)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #61: input, references = 4, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | EXISTS V1: pppp9-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #62: input, references = 5, size of lhs = 7:
% 0.76/0.95     pppp9-{F}(V0), P_relation_dom-{F}(V0,V1), P_identity_relation-{F}(V1,V2), P_relation_composition-{F}(V2,V0,V0), P_relation_rng-{F}(V0,V4), P_identity_relation-{F}(V4,V5), P_relation_composition-{F}(V0,V5,V0) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #63: input, references = 3, size of lhs = 7:
% 0.76/0.95     pppp9-{F}(V0), P_relation_dom-{F}(V0,V1), P_identity_relation-{F}(V1,V2), P_relation_composition-{F}(V2,V0,V3), P_relation_rng-{F}(V0,V4), P_identity_relation-{F}(V4,V5), P_relation_composition-{F}(V0,V5,V6) | function-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #64: input, references = 5, size of lhs = 7:
% 0.76/0.95     pppp9-{F}(V0), P_relation_dom-{F}(V0,V1), P_identity_relation-{F}(V1,V2), P_relation_composition-{F}(V2,V0,V3), P_relation_rng-{F}(V0,V4), P_identity_relation-{F}(V4,V5), P_relation_composition-{F}(V0,V5,V6) | relation-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #65: input, references = 5, size of lhs = 7:
% 0.76/0.95     P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), relation-{F}(V1), P_identity_relation-{F}(V3,V4), P_relation_composition-{F}(V4,V1,V5), subset-{F}(V2,V3), V5 == V1 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #66: input, references = 5, size of lhs = 7:
% 0.76/0.95     P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), relation-{F}(V1), P_identity_relation-{F}(V3,V4), P_relation_composition-{F}(V1,V4,V5), subset-{F}(V2,V3), V5 == V1 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #67: input, references = 4, size of lhs = 0:
% 0.76/0.95     FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #68: input, references = 3, size of lhs = 1:
% 0.76/0.95     #-{F} V0 | EXISTS V1: P_powerset-{T}(V0,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #69: input, references = 5, size of lhs = 1:
% 0.76/0.95     #-{F} V0 | EXISTS V1: P_relation_dom-{T}(V0,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #70: input, references = 5, size of lhs = 1:
% 0.76/0.95     #-{F} V0 | EXISTS V1: P_relation_rng-{T}(V0,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #71: input, references = 11, size of lhs = 2:
% 0.76/0.95     #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_composition-{T}(V0,V1,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #72: input, references = 7, size of lhs = 1:
% 0.76/0.95     #-{F} V0 | EXISTS V1: P_identity_relation-{T}(V0,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  number of initial rules = 73
% 0.76/0.95  
% 0.76/0.95  Simplifiers:
% 0.76/0.95  #73: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #74: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     P_powerset-{F}(V0,V1), P_powerset-{F}(V0,V3), V1 == V3 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #75: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V0,V3), V1 == V3 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #76: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     P_relation_rng-{F}(V0,V1), P_relation_rng-{F}(V0,V3), V1 == V3 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #77: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     P_relation_composition-{F}(V0,V1,V2), P_relation_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #78: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     P_identity_relation-{F}(V0,V1), P_identity_relation-{F}(V0,V3), V1 == V3 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #79: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     pppp0-{F}(V0,V1), pppp0-{F}(V0,V3), V1 == V3 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #80: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     pppp1-{F}(V0), pppp1-{F}(V1), V0 == V1 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #81: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     pppp2-{F}(V0,V1), pppp2-{F}(V2,V1), V0 == V2 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #82: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     pppp3-{F}(V0,V1), pppp3-{F}(V2,V1), V0 == V2 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #83: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     pppp4-{F}(V0), pppp4-{F}(V1), V0 == V1 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #84: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #85: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #86: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     pppp7-{F}(V0), pppp7-{F}(V1), V0 == V1 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #87: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #88: unsound, references = 3, size of lhs = 3:
% 0.76/0.95     pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  number of simplifiers = 16
% 0.76/0.95  
% 0.76/0.95  Learnt:
% 0.76/0.95  #94: mergings( V0 == V2; #91 ), references = 1, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | pppp4-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #96: mergings( V0 == V2; #92 ), references = 1, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), empty-{F}(V1) | pppp4-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #103: mergings( V0 == V2; #100 ), references = 1, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | pppp7-{T}(V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #105: mergings( V0 == V2; #101 ), references = 1, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), empty-{F}(V1) | pppp7-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #116: mergings( V2 == V3; #113 ), references = 1, size of lhs = 2:
% 0.76/0.95     empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_dom-{T}(V0,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #118: mergings( V2 == V3; #114 ), references = 1, size of lhs = 3:
% 0.76/0.95     empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_dom-{T}(V0,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #134: mergings( V0 == V3; #131 ), references = 1, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), V1 == V0 | pppp10-{T}(V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #137: mergings( V0 == V3, V1 == V3; #132 ), references = 1, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, P_powerset-{F}(V0,V2) | pppp10-{T}(V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #154: mergings( V2 == V3; #151 ), references = 1, size of lhs = 2:
% 0.76/0.95     empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_rng-{T}(V0,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #156: mergings( V2 == V3; #152 ), references = 1, size of lhs = 3:
% 0.76/0.95     empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_rng-{T}(V0,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #171: disj( #25, input ), references = 1, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), element-{F}(V1,V1) | empty-{T}(V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #173: mergings( V0 == V3; #170 ), references = 3, size of lhs = 5:
% 0.76/0.95     P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V3,V2), element-{F}(V4,V3) | empty-{T}(V3)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #198: mergings( V3 == V4; #195 ), references = 2, size of lhs = 3:
% 0.76/0.95     relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V0,V1,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #200: mergings( V3 == V4; #196 ), references = 1, size of lhs = 4:
% 0.76/0.95     relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V0,V1,V3)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #212: exists( #71, #66 ), references = 2, size of lhs = 5:
% 0.76/0.95     P_empty_set-{F}(V0), relation-{F}(V1), P_relation_rng-{F}(V1,V2), subset-{F}(V2,V3), P_identity_relation-{F}(V3,V4) | P_relation_composition-{T}(V1,V4,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #221: mergings( V2 == V3, V3 == V4, V5 == V0; #217 ), references = 1, size of lhs = 7:
% 0.76/0.95     empty-{F}(V0), relation-{F}(V0), pppp9-{F}(V0), P_empty_set-{F}(V0), P_relation_dom-{F}(V0,V1), subset-{F}(V1,V1), P_relation_rng-{F}(V0,V1) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #250: mergings( V0 == V3; #246 ), references = 1, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), element-{F}(V1,V2), P_powerset-{F}(V3,V2) | in-{T}(V1,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #252: mergings( V0 == V3; #247 ), references = 1, size of lhs = 3:
% 0.76/0.95     P_empty_set-{F}(V0), element-{F}(V1,V2), V2 == V0 | in-{T}(V1,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #255: mergings( V0 == V3, V2 == V3; #248 ), references = 1, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, element-{F}(V2,V0) | in-{T}(V2,V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #271: mergings( V4 == V8; #269 ), references = 2, size of lhs = 11:
% 0.76/0.95     pppp9-{F}(V0), P_relation_dom-{F}(V0,V1), P_identity_relation-{F}(V1,V2), P_empty_set-{F}(V3), P_relation_rng-{F}(V0,V4), P_identity_relation-{F}(V4,V5), P_relation_composition-{F}(V0,V5,V6), subset-{F}(V4,V7), P_identity_relation-{F}(V7,V8), P_relation_composition-{F}(V0,V8,V9), V9 == V0 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #274: mergings( V5 == V7; #272 ), references = 1, size of lhs = 8:
% 0.76/0.95     pppp9-{F}(V0), P_relation_dom-{F}(V0,V1), P_identity_relation-{F}(V1,V2), P_empty_set-{F}(V3), P_relation_rng-{F}(V0,V4), P_identity_relation-{F}(V4,V5), subset-{F}(V4,V6), P_identity_relation-{F}(V6,V5) | P_relation_composition-{T}(V0,V5,V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #279: mergings( V3 == V8; #277 ), references = 2, size of lhs = 9:
% 0.76/0.95     pppp9-{F}(V0), P_relation_rng-{F}(V0,V1), P_identity_relation-{F}(V1,V2), P_relation_composition-{F}(V0,V2,V3), P_empty_set-{F}(V4), P_relation_dom-{F}(V0,V5), P_identity_relation-{F}(V5,V6), subset-{F}(V5,V7), P_identity_relation-{F}(V7,V6) | P_relation_composition-{T}(V6,V0,V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #292: exists( #71, #65 ), references = 1, size of lhs = 5:
% 0.76/0.95     P_empty_set-{F}(V0), relation-{F}(V1), P_relation_dom-{F}(V1,V2), subset-{F}(V2,V3), P_identity_relation-{F}(V3,V4) | P_relation_composition-{T}(V4,V1,V1)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #299: mergings( V3 == V4; #297 ), references = 1, size of lhs = 3:
% 0.76/0.95     relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V1,V0,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #316: mergings( V0 == V3, V3 == V6; #311 ), references = 2, size of lhs = 5:
% 0.76/0.95     empty-{F}(V0), P_powerset-{F}(V0,V1), P_empty_set-{F}(V2), element-{F}(V3,V1), V3 == V2 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #320: mergings( V0 == V3, V3 == V6, V1 == V6; #313 ), references = 1, size of lhs = 6:
% 0.76/0.95     empty-{F}(V0), P_powerset-{F}(V0,V1), P_empty_set-{F}(V2), element-{F}(V2,V1), empty-{F}(V3), V2 == V3 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #340: mergings( V0 == V4; #338 ), references = 1, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | pppp3-{T}(V0,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #347: mergings( V0 == V4; #345 ), references = 1, size of lhs = 3:
% 0.76/0.95     empty-{F}(V0), P_powerset-{F}(V0,V1), P_empty_set-{F}(V2) | pppp0-{T}(V1,V2)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #355: exists( #72, #271 ), references = 1, size of lhs = 10:
% 0.76/0.95     pppp9-{F}(V0), P_relation_dom-{F}(V0,V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V0,V3), P_identity_relation-{F}(V3,V4), P_relation_composition-{F}(V0,V4,V5), subset-{F}(V3,V6), P_identity_relation-{F}(V6,V7), P_relation_composition-{F}(V0,V7,V8), V8 == V0 | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #357: exists( #71, #354 ), references = 1, size of lhs = 7:
% 0.76/0.95     pppp9-{F}(V0), P_relation_dom-{F}(V0,V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V0,V3), P_identity_relation-{F}(V3,V4), subset-{F}(V3,V5), P_identity_relation-{F}(V5,V4) | P_relation_composition-{T}(V0,V4,V0)
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #371: mergings( V4 == V7, V5 == V8, V6 == V3; #367 ), references = 1, size of lhs = 7:
% 0.76/0.95     P_empty_set-{F}(V0), pppp9-{F}(V1), P_relation_dom-{F}(V1,V2), subset-{F}(V2,V2), P_relation_rng-{F}(V1,V3), P_identity_relation-{F}(V3,V4), P_relation_composition-{F}(V1,V4,V1) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #376: mergings( V2 == V3, V5 == V6; #373 ), references = 2, size of lhs = 6:
% 0.76/0.95     P_empty_set-{F}(V0), pppp9-{F}(V1), P_relation_dom-{F}(V1,V2), subset-{F}(V2,V2), P_relation_rng-{F}(V1,V3), subset-{F}(V3,V3) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #404: mergings( V2 == V3; #402 ), references = 2, size of lhs = 4:
% 0.76/0.95     P_empty_set-{F}(V0), pppp9-{F}(V1), P_relation_dom-{F}(V1,V2), subset-{F}(V2,V2) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #408: mergings( V2 == V3; #406 ), references = 1, size of lhs = 2:
% 0.76/0.95     P_empty_set-{F}(V0), pppp9-{F}(V1) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #412: mergings( V0 == V2, V2 == V3; #409 ), references = 1, size of lhs = 1:
% 0.76/0.95     P_empty_set-{F}(V0) | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  #414: exists( #67, #409 ), references = 1, size of lhs = 0:
% 0.76/0.95     FALSE | FALSE
% 0.76/0.95        (used 0 times, uses = {})
% 0.76/0.95  
% 0.76/0.95  number of learnt formulas = 36
% 0.76/0.95  
% 0.76/0.95  
% 0.76/0.95  % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.76/0.95  
% 0.76/0.95  randbase = 1
%------------------------------------------------------------------------------