%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ016-2.005 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:31:13 PM UTC 2026
% Result : Unsatisfiable 2.78s 1.29s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 88
% Syntax : Number of formulae : 232 ( 40 unt; 37 def)
% Number of atoms : 467 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 492 ( 257 ~; 198 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 75 ( 74 usr; 75 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,negated_conjecture,
~ vertical_1_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uncovered2_1_2) ).
fof(f5,negated_conjecture,
~ horizontal_1_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uncovered3_1_2) ).
fof(f7,negated_conjecture,
( horizontal_1_1
| vertical_1_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_1_1) ).
fof(f9,negated_conjecture,
( vertical_1_5
| horizontal_1_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_1_5) ).
fof(f11,negated_conjecture,
( horizontal_2_2
| vertical_2_2
| horizontal_2_1
| vertical_1_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_2_2) ).
fof(f13,negated_conjecture,
( horizontal_2_4
| vertical_2_4
| horizontal_2_3
| vertical_1_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_2_4) ).
fof(f15,negated_conjecture,
( horizontal_3_1
| vertical_3_1
| vertical_2_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_3_1) ).
fof(f17,negated_conjecture,
( horizontal_3_3
| vertical_3_3
| horizontal_3_2
| vertical_2_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_3_3) ).
fof(f19,negated_conjecture,
( vertical_3_5
| horizontal_3_4
| vertical_2_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_3_5) ).
fof(f21,negated_conjecture,
( horizontal_4_2
| vertical_4_2
| horizontal_4_1
| vertical_3_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_4_2) ).
fof(f23,negated_conjecture,
( horizontal_4_4
| vertical_4_4
| horizontal_4_3
| vertical_3_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_4_4) ).
fof(f25,negated_conjecture,
( horizontal_5_1
| vertical_4_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_5_1) ).
fof(f27,negated_conjecture,
( horizontal_5_3
| horizontal_5_2
| vertical_4_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_5_3) ).
fof(f29,negated_conjecture,
( horizontal_5_4
| vertical_4_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',covered_5_5) ).
fof(f31,negated_conjecture,
( ~ horizontal_1_4
| ~ vertical_1_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover1_1_4) ).
fof(f36,negated_conjecture,
( ~ horizontal_2_1
| ~ vertical_1_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover3_2_1) ).
fof(f37,negated_conjecture,
( ~ vertical_2_1
| ~ vertical_1_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover5_2_1) ).
fof(f44,negated_conjecture,
( ~ horizontal_2_3
| ~ vertical_2_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover1_2_3) ).
fof(f45,negated_conjecture,
( ~ horizontal_2_3
| ~ horizontal_2_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover2_2_3) ).
fof(f47,negated_conjecture,
( ~ vertical_2_3
| ~ horizontal_2_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover4_2_3) ).
fof(f56,negated_conjecture,
( ~ vertical_2_5
| ~ horizontal_2_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover4_2_5) ).
fof(f57,negated_conjecture,
( ~ vertical_2_5
| ~ vertical_1_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover5_2_5) ).
fof(f62,negated_conjecture,
( ~ horizontal_3_2
| ~ vertical_3_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover1_3_2) ).
fof(f63,negated_conjecture,
( ~ horizontal_3_2
| ~ horizontal_3_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover2_3_2) ).
fof(f64,negated_conjecture,
( ~ horizontal_3_2
| ~ vertical_2_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover3_3_2) ).
fof(f65,negated_conjecture,
( ~ vertical_3_2
| ~ horizontal_3_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover4_3_2) ).
fof(f66,negated_conjecture,
( ~ vertical_3_2
| ~ vertical_2_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover5_3_2) ).
fof(f67,negated_conjecture,
( ~ horizontal_3_1
| ~ vertical_2_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover6_3_2) ).
fof(f74,negated_conjecture,
( ~ horizontal_3_4
| ~ vertical_3_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover1_3_4) ).
fof(f75,negated_conjecture,
( ~ horizontal_3_4
| ~ horizontal_3_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover2_3_4) ).
fof(f77,negated_conjecture,
( ~ vertical_3_4
| ~ horizontal_3_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover4_3_4) ).
fof(f78,negated_conjecture,
( ~ vertical_3_4
| ~ vertical_2_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover5_3_4) ).
fof(f79,negated_conjecture,
( ~ horizontal_3_3
| ~ vertical_2_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover6_3_4) ).
fof(f83,negated_conjecture,
( ~ horizontal_4_1
| ~ vertical_4_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover1_4_1) ).
fof(f84,negated_conjecture,
( ~ horizontal_4_1
| ~ vertical_3_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover3_4_1) ).
fof(f85,negated_conjecture,
( ~ vertical_4_1
| ~ vertical_3_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover5_4_1) ).
fof(f92,negated_conjecture,
( ~ horizontal_4_3
| ~ vertical_4_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover1_4_3) ).
fof(f93,negated_conjecture,
( ~ horizontal_4_3
| ~ horizontal_4_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover2_4_3) ).
fof(f94,negated_conjecture,
( ~ horizontal_4_3
| ~ vertical_3_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover3_4_3) ).
fof(f95,negated_conjecture,
( ~ vertical_4_3
| ~ horizontal_4_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover4_4_3) ).
fof(f96,negated_conjecture,
( ~ vertical_4_3
| ~ vertical_3_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover5_4_3) ).
fof(f97,negated_conjecture,
( ~ horizontal_4_2
| ~ vertical_3_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover6_4_3) ).
fof(f104,negated_conjecture,
( ~ vertical_4_5
| ~ horizontal_4_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover4_4_5) ).
fof(f105,negated_conjecture,
( ~ vertical_4_5
| ~ vertical_3_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover5_4_5) ).
fof(f106,negated_conjecture,
( ~ horizontal_4_4
| ~ vertical_3_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover6_4_5) ).
fof(f108,negated_conjecture,
( ~ horizontal_5_2
| ~ horizontal_5_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover2_5_2) ).
fof(f109,negated_conjecture,
( ~ horizontal_5_2
| ~ vertical_4_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover3_5_2) ).
fof(f110,negated_conjecture,
( ~ horizontal_5_1
| ~ vertical_4_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover6_5_2) ).
fof(f114,negated_conjecture,
( ~ horizontal_5_4
| ~ horizontal_5_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover2_5_4) ).
fof(f115,negated_conjecture,
( ~ horizontal_5_4
| ~ vertical_4_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover3_5_4) ).
fof(f116,negated_conjecture,
( ~ horizontal_5_3
| ~ vertical_4_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_cover6_5_4) ).
fof(f119,definition,
( spl0_1
<=> vertical_4_5 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f122,definition,
( spl0_2
<=> horizontal_5_4 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f126,definition,
( spl0_3
<=> vertical_4_4 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f129,definition,
( spl0_4
<=> horizontal_5_3 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f131,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f116,f129,f126]) ).
fof(f132,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f115,f122,f126]) ).
fof(f133,plain,
( ~ spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f114,f122,f129]) ).
fof(f135,definition,
( spl0_5
<=> vertical_4_3 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f138,definition,
( spl0_6
<=> horizontal_5_2 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f144,definition,
( spl0_7
<=> vertical_4_2 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f147,definition,
( spl0_8
<=> horizontal_5_1 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f149,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f110,f147,f144]) ).
fof(f150,plain,
( ~ spl0_7
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f109,f138,f144]) ).
fof(f151,plain,
( ~ spl0_8
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f108,f138,f147]) ).
fof(f153,definition,
( spl0_9
<=> vertical_4_1 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f157,definition,
( spl0_10
<=> vertical_3_5 ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f160,definition,
( spl0_11
<=> horizontal_4_4 ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f162,plain,
( ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f106,f160,f157]) ).
fof(f163,plain,
( ~ spl0_10
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f105,f119,f157]) ).
fof(f164,plain,
( ~ spl0_11
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f104,f119,f160]) ).
fof(f166,definition,
( spl0_12
<=> vertical_3_4 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f169,definition,
( spl0_13
<=> horizontal_4_3 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f178,definition,
( spl0_14
<=> vertical_3_3 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f181,definition,
( spl0_15
<=> horizontal_4_2 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f183,plain,
( ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f97,f181,f178]) ).
fof(f184,plain,
( ~ spl0_14
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f96,f135,f178]) ).
fof(f185,plain,
( ~ spl0_15
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f95,f135,f181]) ).
fof(f186,plain,
( ~ spl0_14
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f94,f169,f178]) ).
fof(f187,plain,
( ~ spl0_15
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f93,f169,f181]) ).
fof(f188,plain,
( ~ spl0_5
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f92,f169,f135]) ).
fof(f190,definition,
( spl0_16
<=> vertical_3_2 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f193,definition,
( spl0_17
<=> horizontal_4_1 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f202,definition,
( spl0_18
<=> vertical_3_1 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f204,plain,
( ~ spl0_18
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f85,f153,f202]) ).
fof(f205,plain,
( ~ spl0_18
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f84,f193,f202]) ).
fof(f206,plain,
( ~ spl0_9
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f83,f193,f153]) ).
fof(f208,definition,
( spl0_19
<=> vertical_2_5 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f211,definition,
( spl0_20
<=> horizontal_3_4 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f217,definition,
( spl0_21
<=> vertical_2_4 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f220,definition,
( spl0_22
<=> horizontal_3_3 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f222,plain,
( ~ spl0_21
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f79,f220,f217]) ).
fof(f223,plain,
( ~ spl0_21
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f78,f166,f217]) ).
fof(f224,plain,
( ~ spl0_22
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f77,f166,f220]) ).
fof(f226,plain,
( ~ spl0_22
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f75,f211,f220]) ).
fof(f227,plain,
( ~ spl0_12
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f74,f211,f166]) ).
fof(f229,definition,
( spl0_23
<=> vertical_2_3 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f232,definition,
( spl0_24
<=> horizontal_3_2 ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f241,definition,
( spl0_25
<=> vertical_2_2 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f244,definition,
( spl0_26
<=> horizontal_3_1 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f246,plain,
( ~ spl0_25
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f67,f244,f241]) ).
fof(f247,plain,
( ~ spl0_25
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f66,f190,f241]) ).
fof(f248,plain,
( ~ spl0_26
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f65,f190,f244]) ).
fof(f249,plain,
( ~ spl0_25
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f64,f232,f241]) ).
fof(f250,plain,
( ~ spl0_26
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f63,f232,f244]) ).
fof(f251,plain,
( ~ spl0_16
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f62,f232,f190]) ).
fof(f253,definition,
( spl0_27
<=> vertical_2_1 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f259,definition,
( spl0_28
<=> vertical_1_5 ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f262,definition,
( spl0_29
<=> horizontal_2_4 ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f265,plain,
( ~ spl0_28
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f57,f208,f259]) ).
fof(f266,plain,
( ~ spl0_29
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f56,f208,f262]) ).
fof(f268,definition,
( spl0_30
<=> vertical_1_4 ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f271,definition,
( spl0_31
<=> horizontal_2_3 ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f283,definition,
( spl0_33
<=> horizontal_2_2 ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f287,plain,
( ~ spl0_33
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f47,f229,f283]) ).
fof(f289,plain,
( ~ spl0_33
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f45,f271,f283]) ).
fof(f290,plain,
( ~ spl0_23
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f44,f271,f229]) ).
fof(f292,definition,
( spl0_34
<=> vertical_1_2 ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f295,definition,
( spl0_35
<=> horizontal_2_1 ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f304,definition,
( spl0_36
<=> vertical_1_1 ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f306,plain,
( ~ spl0_36
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f37,f253,f304]) ).
fof(f307,plain,
( ~ spl0_36
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f36,f295,f304]) ).
fof(f310,definition,
( spl0_37
<=> horizontal_1_4 ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f318,plain,
( ~ spl0_30
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f31,f310,f268]) ).
fof(f320,definition,
( spl0_39
<=> horizontal_1_1 ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f325,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f29,f122,f119]) ).
fof(f331,plain,
( spl0_5
| spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f27,f129,f138,f135]) ).
fof(f336,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f25,f147,f153]) ).
fof(f342,plain,
( spl0_12
| spl0_13
| spl0_3
| spl0_11 ),
inference(avatar_split_clause,[],[f23,f160,f126,f169,f166]) ).
fof(f348,plain,
( spl0_16
| spl0_17
| spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f21,f181,f144,f193,f190]) ).
fof(f353,plain,
( spl0_19
| spl0_20
| spl0_10 ),
inference(avatar_split_clause,[],[f19,f157,f211,f208]) ).
fof(f359,plain,
( spl0_23
| spl0_24
| spl0_14
| spl0_22 ),
inference(avatar_split_clause,[],[f17,f220,f178,f232,f229]) ).
fof(f364,plain,
( spl0_27
| spl0_18
| spl0_26 ),
inference(avatar_split_clause,[],[f15,f244,f202,f253]) ).
fof(f370,plain,
( spl0_30
| spl0_31
| spl0_21
| spl0_29 ),
inference(avatar_split_clause,[],[f13,f262,f217,f271,f268]) ).
fof(f376,plain,
( spl0_34
| spl0_35
| spl0_25
| spl0_33 ),
inference(avatar_split_clause,[],[f11,f283,f241,f295,f292]) ).
fof(f380,plain,
( spl0_37
| spl0_28 ),
inference(avatar_split_clause,[],[f9,f259,f310]) ).
fof(f384,plain,
( spl0_36
| spl0_39 ),
inference(avatar_split_clause,[],[f7,f320,f304]) ).
fof(f385,plain,
~ spl0_39,
inference(avatar_split_clause,[],[f5,f320]) ).
fof(f387,plain,
~ spl0_34,
inference(avatar_split_clause,[],[f3,f292]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f131]) ).
cnf(s3,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f132]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f133]) ).
cnf(s8,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f149]) ).
cnf(s9,plain,
( ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f150]) ).
cnf(s10,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f151]) ).
cnf(s12,plain,
( ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f162]) ).
cnf(s13,plain,
( ~ spl0_1
| ~ spl0_10 ),
inference(sat_conversion,[],[f163]) ).
cnf(s14,plain,
( ~ spl0_1
| ~ spl0_11 ),
inference(sat_conversion,[],[f164]) ).
cnf(s21,plain,
( ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f183]) ).
cnf(s22,plain,
( ~ spl0_5
| ~ spl0_14 ),
inference(sat_conversion,[],[f184]) ).
cnf(s23,plain,
( ~ spl0_5
| ~ spl0_15 ),
inference(sat_conversion,[],[f185]) ).
cnf(s24,plain,
( ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f186]) ).
cnf(s25,plain,
( ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f187]) ).
cnf(s26,plain,
( ~ spl0_5
| ~ spl0_13 ),
inference(sat_conversion,[],[f188]) ).
cnf(s33,plain,
( ~ spl0_9
| ~ spl0_18 ),
inference(sat_conversion,[],[f204]) ).
cnf(s34,plain,
( ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f205]) ).
cnf(s35,plain,
( ~ spl0_9
| ~ spl0_17 ),
inference(sat_conversion,[],[f206]) ).
cnf(s39,plain,
( ~ spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f222]) ).
cnf(s40,plain,
( ~ spl0_12
| ~ spl0_21 ),
inference(sat_conversion,[],[f223]) ).
cnf(s41,plain,
( ~ spl0_12
| ~ spl0_22 ),
inference(sat_conversion,[],[f224]) ).
cnf(s43,plain,
( ~ spl0_20
| ~ spl0_22 ),
inference(sat_conversion,[],[f226]) ).
cnf(s44,plain,
( ~ spl0_12
| ~ spl0_20 ),
inference(sat_conversion,[],[f227]) ).
cnf(s51,plain,
( ~ spl0_25
| ~ spl0_26 ),
inference(sat_conversion,[],[f246]) ).
cnf(s52,plain,
( ~ spl0_16
| ~ spl0_25 ),
inference(sat_conversion,[],[f247]) ).
cnf(s53,plain,
( ~ spl0_16
| ~ spl0_26 ),
inference(sat_conversion,[],[f248]) ).
cnf(s54,plain,
( ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f249]) ).
cnf(s55,plain,
( ~ spl0_24
| ~ spl0_26 ),
inference(sat_conversion,[],[f250]) ).
cnf(s56,plain,
( ~ spl0_16
| ~ spl0_24 ),
inference(sat_conversion,[],[f251]) ).
cnf(s61,plain,
( ~ spl0_19
| ~ spl0_28 ),
inference(sat_conversion,[],[f265]) ).
cnf(s62,plain,
( ~ spl0_19
| ~ spl0_29 ),
inference(sat_conversion,[],[f266]) ).
cnf(s71,plain,
( ~ spl0_23
| ~ spl0_33 ),
inference(sat_conversion,[],[f287]) ).
cnf(s73,plain,
( ~ spl0_31
| ~ spl0_33 ),
inference(sat_conversion,[],[f289]) ).
cnf(s74,plain,
( ~ spl0_23
| ~ spl0_31 ),
inference(sat_conversion,[],[f290]) ).
cnf(s81,plain,
( ~ spl0_27
| ~ spl0_36 ),
inference(sat_conversion,[],[f306]) ).
cnf(s82,plain,
( ~ spl0_35
| ~ spl0_36 ),
inference(sat_conversion,[],[f307]) ).
cnf(s87,plain,
( ~ spl0_30
| ~ spl0_37 ),
inference(sat_conversion,[],[f318]) ).
cnf(s89,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f325]) ).
cnf(s91,plain,
( spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f331]) ).
cnf(s93,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f336]) ).
cnf(s95,plain,
( spl0_3
| spl0_11
| spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f342]) ).
cnf(s97,plain,
( spl0_7
| spl0_15
| spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f348]) ).
cnf(s99,plain,
( spl0_10
| spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f353]) ).
cnf(s101,plain,
( spl0_14
| spl0_22
| spl0_23
| spl0_24 ),
inference(sat_conversion,[],[f359]) ).
cnf(s103,plain,
( spl0_18
| spl0_26
| spl0_27 ),
inference(sat_conversion,[],[f364]) ).
cnf(s105,plain,
( spl0_21
| spl0_29
| spl0_30
| spl0_31 ),
inference(sat_conversion,[],[f370]) ).
cnf(s107,plain,
( spl0_25
| spl0_33
| spl0_34
| spl0_35 ),
inference(sat_conversion,[],[f376]) ).
cnf(s109,plain,
( spl0_28
| spl0_37 ),
inference(sat_conversion,[],[f380]) ).
cnf(s111,plain,
( spl0_36
| spl0_39 ),
inference(sat_conversion,[],[f384]) ).
cnf(s112,plain,
~ spl0_39,
inference(sat_conversion,[],[f385]) ).
cnf(s114,plain,
~ spl0_34,
inference(sat_conversion,[],[f387]) ).
cnf(s116,plain,
spl0_36,
inference(rat,[],[s111,s112]) ).
cnf(s118,plain,
( spl0_25
| spl0_33
| spl0_35 ),
inference(rat,[],[s107,s114]) ).
cnf(s120,plain,
~ spl0_35,
inference(rat,[],[s82,s116]) ).
cnf(s121,plain,
~ spl0_27,
inference(rat,[],[s81,s116]) ).
cnf(s122,plain,
( ~ spl0_6
| spl0_3 ),
inference(rat,[],[s87,s109,s105,s61,s62,s99,s12,s95,s39,s41,s43,s101,s71,s73,s21,s25,s118,s97,s51,s53,s55,s103,s33,s35,s93,s9,s10,s120,s121]) ).
cnf(s123,plain,
( ~ spl0_26
| spl0_10
| spl0_14 ),
inference(rat,[],[s87,s109,s105,s61,s62,s99,s39,s43,s101,s71,s73,s118,s51,s55,s120]) ).
cnf(s124,plain,
( spl0_10
| spl0_7
| ~ spl0_5 ),
inference(rat,[],[s87,s109,s105,s61,s62,s99,s39,s43,s101,s71,s73,s118,s52,s56,s97,s34,s103,s123,s23,s22,s120,s121]) ).
cnf(s125,plain,
( ~ spl0_26
| spl0_22
| spl0_14 ),
inference(rat,[],[s71,s118,s101,s51,s55,s120]) ).
cnf(s126,plain,
( spl0_7
| ~ spl0_2 ),
inference(rat,[],[s71,s118,s101,s52,s56,s97,s34,s103,s125,s41,s95,s12,s124,s26,s23,s22,s91,s122,s3,s4,s120,s121]) ).
cnf(s127,plain,
~ spl0_2,
inference(rat,[],[s95,s41,s12,s125,s123,s103,s33,s93,s8,s126,s22,s26,s91,s122,s3,s4,s121]) ).
cnf(s128,plain,
spl0_1,
inference(rat,[],[s89,s127]) ).
cnf(s129,plain,
~ spl0_11,
inference(rat,[],[s14,s128]) ).
cnf(s130,plain,
~ spl0_10,
inference(rat,[],[s13,s128]) ).
cnf(s131,plain,
~ spl0_5,
inference(rat,[],[s33,s93,s103,s8,s123,s124,s22,s121,s130]) ).
cnf(s132,plain,
( ~ spl0_23
| ~ spl0_18 ),
inference(rat,[],[s87,s109,s105,s61,s62,s99,s40,s44,s95,s25,s97,s52,s118,s71,s74,s34,s8,s2,s91,s10,s93,s33,s130,s129,s120,s131]) ).
cnf(s133,plain,
( ~ spl0_24
| ~ spl0_18 ),
inference(rat,[],[s87,s109,s105,s61,s62,s99,s40,s44,s95,s73,s25,s118,s97,s54,s56,s34,s8,s2,s91,s10,s93,s33,s130,s129,s120,s131]) ).
cnf(s134,plain,
spl0_14,
inference(rat,[],[s73,s118,s105,s52,s87,s97,s109,s25,s61,s62,s95,s99,s39,s41,s43,s101,s133,s132,s2,s91,s8,s10,s93,s33,s34,s103,s123,s120,s129,s130,s131,s121]) ).
cnf(s138,plain,
~ spl0_13,
inference(rat,[],[s24,s134]) ).
cnf(s139,plain,
~ spl0_15,
inference(rat,[],[s21,s134]) ).
cnf(s140,plain,
~ spl0_17,
inference(rat,[],[s87,s109,s105,s61,s62,s99,s40,s44,s95,s73,s2,s118,s91,s51,s10,s103,s93,s34,s35,s130,s129,s138,s120,s131,s121]) ).
cnf(s141,plain,
~ spl0_26,
inference(rat,[],[s87,s109,s105,s61,s62,s99,s40,s44,s95,s2,s91,s73,s9,s118,s97,s51,s53,s130,s129,s138,s131,s120,s139,s140]) ).
cnf(s142,plain,
spl0_18,
inference(rat,[],[s103,s121,s141]) ).
cnf(s143,plain,
~ spl0_9,
inference(rat,[],[s33,s142]) ).
cnf(s144,plain,
spl0_8,
inference(rat,[],[s93,s143]) ).
cnf(s145,plain,
~ spl0_6,
inference(rat,[],[s10,s144]) ).
cnf(s146,plain,
~ spl0_7,
inference(rat,[],[s8,s144]) ).
cnf(s147,plain,
spl0_4,
inference(rat,[],[s91,s131,s145]) ).
cnf(s148,plain,
spl0_16,
inference(rat,[],[s97,s140,s139,s146]) ).
cnf(s149,plain,
~ spl0_3,
inference(rat,[],[s2,s147]) ).
cnf(s150,plain,
~ spl0_25,
inference(rat,[],[s52,s148]) ).
cnf(s151,plain,
spl0_12,
inference(rat,[],[s95,s138,s129,s149]) ).
cnf(s152,plain,
spl0_33,
inference(rat,[],[s118,s120,s150]) ).
cnf(s153,plain,
~ spl0_20,
inference(rat,[],[s44,s151]) ).
cnf(s154,plain,
~ spl0_21,
inference(rat,[],[s40,s151]) ).
cnf(s155,plain,
~ spl0_31,
inference(rat,[],[s73,s152]) ).
cnf(s156,plain,
spl0_19,
inference(rat,[],[s99,s130,s153]) ).
cnf(s157,plain,
~ spl0_29,
inference(rat,[],[s62,s156]) ).
cnf(s158,plain,
~ spl0_28,
inference(rat,[],[s61,s156]) ).
cnf(s159,plain,
spl0_30,
inference(rat,[],[s105,s155,s154,s157]) ).
cnf(s160,plain,
spl0_37,
inference(rat,[],[s109,s158]) ).
cnf(s161,plain,
$false,
inference(rat,[],[s87,s160,s159]) ).
fof(f389,plain,
$false,
inference(avatar_sat_refutation,[],[s161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ016-2.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 22:31:27 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.78/1.29 % (983642)Input is clausal, will run a generic CNF schedule.
% 2.78/1.29 % (983647)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3377993415:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.78/1.29 % (983651)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1635225305:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.78/1.29 % (983649)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2595299123:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.78/1.29 % (983650)lrs+10_1_sil=8000:sp=occurrence:random_seed=4007634301:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.78/1.29 % (983648)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=131437898:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.78/1.29 % (983652)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1595081528:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.78/1.29 % (983650)Also succeeded, but the first one will report.
% 2.78/1.29 % (983652)Also succeeded, but the first one will report.
% 2.78/1.29 % (983651)First to succeed.
% 2.78/1.29 % (983651)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-983642"
% 2.78/1.29 % (983653)dis-21_1_sil=8000:lcm=predicate:random_seed=586650197:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.78/1.29 % (983653)Also succeeded, but the first one will report.
% 2.78/1.29 [W927 22:31:27.092991293 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 2.78/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.78/1.29 [W927 22:31:27.093035765 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 2.78/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.78/1.29 [W927 22:31:27.093055778 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 2.78/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.78/1.29 [W927 22:31:27.093061758 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 2.78/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.78/1.29 [W927 22:31:27.093075148 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 2.78/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.78/1.29 [W927 22:31:27.093080840 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 2.78/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.78/1.29 [W927 22:31:27.093099504 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 2.78/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.78/1.29 [W927 22:31:27.093106009 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 2.78/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.78/1.29 % (983651)Refutation found. Thanks to Tanya!
% 2.78/1.29 % SZS status Unsatisfiable for theBenchmark
% 2.78/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.48 % (983651)------------------------------
% 3.60/1.48 % (983651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.48 % (983651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.48 % (983651)CaDiCaL version: 2.1.3
% 3.60/1.48 % (983651)Termination reason: Refutation
% 3.60/1.48 % (983651)Time elapsed: 0.004 s
% 3.60/1.48 % (983651)Peak memory usage: 88 MB
% 3.60/1.48 % (983651)Instructions burned: 5 (million)
% 3.60/1.48 % (983651)------------------------------
% 3.60/1.48 % (983651)------------------------------
% 3.60/1.48 % (983642)Success in time 0.431 s
% 3.60/1.48 % Vampire exiting
%------------------------------------------------------------------------------