TSTP Solution File: SYO040_8 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO040_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 : Tue May 21 09:10:04 EDT 2024
% Result : Theorem 0.12s 0.38s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 44
% Syntax : Number of formulae : 243 ( 10 unt; 8 typ; 0 def)
% Number of atoms : 1002 ( 158 equ)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 728 ( 328 ~; 361 |; 6 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 389 ( 369 fml; 20 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of predicates : 38 ( 35 usr; 36 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 10 ( 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
h: $o > $i ).
tff(func_def_3,type,
bG0: $o ).
tff(func_def_4,type,
bG1: $o ).
tff(func_def_5,type,
bG2: $o ).
tff(func_def_6,type,
bG3: $o ).
tff(func_def_7,type,
bG4: $o ).
tff(func_def_8,type,
bG5: $o ).
tff(pred_def_1,type,
f: $o > $o ).
tff(f778,plain,
$false,
inference(avatar_sat_refutation,[],[f36,f41,f50,f55,f64,f73,f82,f91,f95,f120,f129,f136,f139,f142,f148,f154,f156,f161,f165,f167,f172,f177,f181,f188,f192,f202,f204,f216,f217,f219,f229,f248,f354,f360,f368,f376,f381,f395,f412,f423,f434,f451,f456,f459,f473,f487,f517,f522,f560,f567,f580,f586,f588,f613,f647,f657,f658,f679,f726,f735,f777]) ).
tff(f777,plain,
( ~ spl6_16
| spl6_10
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f240,f174,f75,f126]) ).
tff(f126,plain,
( spl6_16
<=> f($false) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).
tff(f75,plain,
( spl6_10
<=> f(bG1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
tff(f174,plain,
( spl6_21
<=> ( $false = bG1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_21])]) ).
tff(f240,plain,
( ~ f($false)
| spl6_10
| ~ spl6_21 ),
inference(superposition,[],[f77,f176]) ).
tff(f176,plain,
( ( $false = bG1 )
| ~ spl6_21 ),
inference(avatar_component_clause,[],[f174]) ).
tff(f77,plain,
( ~ f(bG1)
| spl6_10 ),
inference(avatar_component_clause,[],[f75]) ).
tff(f735,plain,
( ~ spl6_9
| spl6_27 ),
inference(avatar_contradiction_clause,[],[f734]) ).
tff(f734,plain,
( $false
| ~ spl6_9
| spl6_27 ),
inference(trivial_inequality_removal,[],[f727]) ).
tff(f727,plain,
( ( h($true) != h($true) )
| ~ spl6_9
| spl6_27 ),
inference(superposition,[],[f559,f72]) ).
tff(f72,plain,
( ( $true = bG3 )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f70]) ).
tff(f70,plain,
( spl6_9
<=> ( $true = bG3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
tff(f559,plain,
( ( h(bG3) != h($true) )
| spl6_27 ),
inference(avatar_component_clause,[],[f557]) ).
tff(f557,plain,
( spl6_27
<=> ( h(bG3) = h($true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_27])]) ).
tff(f726,plain,
( ~ spl6_7
| spl6_18
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f195,f47,f145,f61]) ).
tff(f61,plain,
( spl6_7
<=> ( $true = bG5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
tff(f145,plain,
( spl6_18
<=> f($true) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).
tff(f47,plain,
( spl6_4
<=> ( $true = bG4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
tff(f195,plain,
( f($true)
| ( $true != bG5 )
| ~ spl6_4 ),
inference(forward_demodulation,[],[f20,f49]) ).
tff(f49,plain,
( ( $true = bG4 )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f47]) ).
tff(f20,plain,
( f(bG4)
| ( $true != bG5 ) ),
inference(cnf_transformation,[],[f13]) ).
tff(f13,plain,
( ( f(bG4)
| ( $true != bG5 ) )
& ( ( $true = bG5 )
| ~ f(bG4) ) ),
inference(nnf_transformation,[],[f10]) ).
tff(f10,plain,
( f(bG4)
<=> ( $true = bG5 ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG5])]) ).
tff(f679,plain,
( spl6_18
| ~ spl6_4
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f667,f61,f47,f145]) ).
tff(f667,plain,
( f($true)
| ~ spl6_4
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f666]) ).
tff(f666,plain,
( ( $true != $true )
| f($true)
| ~ spl6_4
| ~ spl6_7 ),
inference(forward_demodulation,[],[f651,f63]) ).
tff(f63,plain,
( ( $true = bG5 )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f61]) ).
tff(f651,plain,
( f($true)
| ( $true != bG5 )
| ~ spl6_4 ),
inference(forward_demodulation,[],[f20,f49]) ).
tff(f658,plain,
( ~ spl6_18
| spl6_10
| ~ spl6_13 ),
inference(avatar_split_clause,[],[f479,f88,f75,f145]) ).
tff(f88,plain,
( spl6_13
<=> ( $true = bG1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).
tff(f479,plain,
( ~ f($true)
| spl6_10
| ~ spl6_13 ),
inference(forward_demodulation,[],[f77,f90]) ).
tff(f90,plain,
( ( $true = bG1 )
| ~ spl6_13 ),
inference(avatar_component_clause,[],[f88]) ).
tff(f657,plain,
( spl6_19
| ~ spl6_25
| ~ spl6_26 ),
inference(avatar_split_clause,[],[f566,f453,f352,f151]) ).
tff(f151,plain,
( spl6_19
<=> ( $false = bG3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_19])]) ).
tff(f352,plain,
( spl6_25
<=> ! [X0: $o] :
( ( h($false) != h((X0)) )
| ( $false = (X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_25])]) ).
tff(f453,plain,
( spl6_26
<=> ( h(bG3) = h($false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_26])]) ).
tff(f566,plain,
( ( $false = bG3 )
| ~ spl6_25
| ~ spl6_26 ),
inference(trivial_inequality_removal,[],[f565]) ).
tff(f565,plain,
( ( h($false) != h($false) )
| ( $false = bG3 )
| ~ spl6_25
| ~ spl6_26 ),
inference(superposition,[],[f353,f454]) ).
tff(f454,plain,
( ( h(bG3) = h($false) )
| ~ spl6_26 ),
inference(avatar_component_clause,[],[f453]) ).
tff(f353,plain,
( ! [X0: $o] :
( ( h($false) != h((X0)) )
| ( $false = (X0) ) )
| ~ spl6_25 ),
inference(avatar_component_clause,[],[f352]) ).
tff(f647,plain,
( ~ spl6_4
| ~ spl6_14
| ~ spl6_17 ),
inference(avatar_contradiction_clause,[],[f646]) ).
tff(f646,plain,
( $false
| ~ spl6_4
| ~ spl6_14
| ~ spl6_17 ),
inference(trivial_inequality_removal,[],[f645]) ).
tff(f645,plain,
( ( $true = $false )
| ~ spl6_4
| ~ spl6_14
| ~ spl6_17 ),
inference(forward_demodulation,[],[f49,f571]) ).
tff(f571,plain,
( ( $false = bG4 )
| ~ spl6_14
| ~ spl6_17 ),
inference(trivial_inequality_removal,[],[f232]) ).
tff(f232,plain,
( ( $true = $false )
| ( $false = bG4 )
| ~ spl6_14
| ~ spl6_17 ),
inference(superposition,[],[f135,f94]) ).
tff(f94,plain,
( ! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) )
| ~ spl6_14 ),
inference(avatar_component_clause,[],[f93]) ).
tff(f93,plain,
( spl6_14
<=> ! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).
tff(f135,plain,
( ( $false = bG4 )
| ~ spl6_17 ),
inference(avatar_component_clause,[],[f133]) ).
tff(f133,plain,
( spl6_17
<=> ( $false = bG4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_17])]) ).
tff(f613,plain,
( spl6_16
| ~ spl6_12
| ~ spl6_14
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f587,f226,f93,f84,f126]) ).
tff(f84,plain,
( spl6_12
<=> f(bG0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
tff(f226,plain,
( spl6_23
<=> ( $false = bG0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_23])]) ).
tff(f587,plain,
( f($false)
| ~ spl6_12
| ~ spl6_14
| ~ spl6_23 ),
inference(forward_demodulation,[],[f85,f574]) ).
tff(f574,plain,
( ( $false = bG0 )
| ~ spl6_14
| ~ spl6_23 ),
inference(trivial_inequality_removal,[],[f242]) ).
tff(f242,plain,
( ( $true = $false )
| ( $false = bG0 )
| ~ spl6_14
| ~ spl6_23 ),
inference(superposition,[],[f228,f94]) ).
tff(f228,plain,
( ( $false = bG0 )
| ~ spl6_23 ),
inference(avatar_component_clause,[],[f226]) ).
tff(f85,plain,
( f(bG0)
| ~ spl6_12 ),
inference(avatar_component_clause,[],[f84]) ).
tff(f588,plain,
( spl6_18
| ~ spl6_10
| ~ spl6_13 ),
inference(avatar_split_clause,[],[f504,f88,f75,f145]) ).
tff(f504,plain,
( f($true)
| ~ spl6_10
| ~ spl6_13 ),
inference(forward_demodulation,[],[f76,f90]) ).
tff(f76,plain,
( f(bG1)
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f75]) ).
tff(f586,plain,
( spl6_12
| ~ spl6_13 ),
inference(avatar_split_clause,[],[f213,f88,f84]) ).
tff(f213,plain,
( f(bG0)
| ~ spl6_13 ),
inference(trivial_inequality_removal,[],[f212]) ).
tff(f212,plain,
( ( $true != $true )
| f(bG0)
| ~ spl6_13 ),
inference(forward_demodulation,[],[f28,f90]) ).
tff(f28,plain,
( f(bG0)
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f17]) ).
tff(f17,plain,
( ( f(bG0)
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ~ f(bG0) ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f6,plain,
( f(bG0)
<=> ( $true = bG1 ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG1])]) ).
tff(f580,plain,
( ~ spl6_3
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f577,f226,f43]) ).
tff(f43,plain,
( spl6_3
<=> x ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
tff(f577,plain,
( ~ x
| ~ spl6_23 ),
inference(trivial_inequality_removal,[],[f499]) ).
tff(f499,plain,
( ( $true = $false )
| ~ x
| ~ spl6_23 ),
inference(forward_demodulation,[],[f29,f228]) ).
tff(f29,plain,
( ( $true = bG0 )
| ~ x ),
inference(cnf_transformation,[],[f18]) ).
tff(f18,plain,
( ( x
| ( $true != bG0 ) )
& ( ( $true = bG0 )
| ~ x ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f5,plain,
( x
<=> ( $true = bG0 ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG0])]) ).
tff(f567,plain,
( ~ spl6_18
| spl6_8
| ~ spl6_11
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f511,f93,f79,f66,f145]) ).
tff(f66,plain,
( spl6_8
<=> f(bG2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
tff(f79,plain,
( spl6_11
<=> ( $true = bG2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
tff(f511,plain,
( ~ f($true)
| spl6_8
| ~ spl6_11
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f510]) ).
tff(f510,plain,
( ( $true = $false )
| ~ f($true)
| spl6_8
| ~ spl6_11
| ~ spl6_14 ),
inference(forward_demodulation,[],[f186,f81]) ).
tff(f81,plain,
( ( $true = bG2 )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f79]) ).
tff(f186,plain,
( ~ f($true)
| ( $false = bG2 )
| spl6_8
| ~ spl6_14 ),
inference(superposition,[],[f68,f94]) ).
tff(f68,plain,
( ~ f(bG2)
| spl6_8 ),
inference(avatar_component_clause,[],[f66]) ).
tff(f560,plain,
( spl6_15
| ~ spl6_27
| spl6_1
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f108,f93,f33,f557,f117]) ).
tff(f117,plain,
( spl6_15
<=> ( $false = bG5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).
tff(f33,plain,
( spl6_1
<=> ( h(bG3) = h(bG5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
tff(f108,plain,
( ( h(bG3) != h($true) )
| ( $false = bG5 )
| spl6_1
| ~ spl6_14 ),
inference(superposition,[],[f35,f94]) ).
tff(f35,plain,
( ( h(bG3) != h(bG5) )
| spl6_1 ),
inference(avatar_component_clause,[],[f33]) ).
tff(f522,plain,
( spl6_6
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f209,f61,f57]) ).
tff(f57,plain,
( spl6_6
<=> f(bG4) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
tff(f209,plain,
( f(bG4)
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f208]) ).
tff(f208,plain,
( ( $true != $true )
| f(bG4)
| ~ spl6_7 ),
inference(forward_demodulation,[],[f20,f63]) ).
tff(f517,plain,
( ~ spl6_5
| ~ spl6_23 ),
inference(avatar_contradiction_clause,[],[f516]) ).
tff(f516,plain,
( $false
| ~ spl6_5
| ~ spl6_23 ),
inference(trivial_inequality_removal,[],[f515]) ).
tff(f515,plain,
( ( $true = $false )
| ~ spl6_5
| ~ spl6_23 ),
inference(forward_demodulation,[],[f53,f228]) ).
tff(f53,plain,
( ( $true = bG0 )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f52]) ).
tff(f52,plain,
( spl6_5
<=> ( $true = bG0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
tff(f487,plain,
( ~ spl6_16
| spl6_6
| ~ spl6_17 ),
inference(avatar_split_clause,[],[f388,f133,f57,f126]) ).
tff(f388,plain,
( ~ f($false)
| spl6_6
| ~ spl6_17 ),
inference(forward_demodulation,[],[f59,f135]) ).
tff(f59,plain,
( ~ f(bG4)
| spl6_6 ),
inference(avatar_component_clause,[],[f57]) ).
tff(f473,plain,
( ~ spl6_13
| ~ spl6_21 ),
inference(avatar_contradiction_clause,[],[f472]) ).
tff(f472,plain,
( $false
| ~ spl6_13
| ~ spl6_21 ),
inference(trivial_inequality_removal,[],[f471]) ).
tff(f471,plain,
( ( $true = $false )
| ~ spl6_13
| ~ spl6_21 ),
inference(forward_demodulation,[],[f90,f176]) ).
tff(f459,plain,
( ~ spl6_14
| ~ spl6_19
| spl6_26 ),
inference(avatar_contradiction_clause,[],[f458]) ).
tff(f458,plain,
( $false
| ~ spl6_14
| ~ spl6_19
| spl6_26 ),
inference(trivial_inequality_removal,[],[f457]) ).
tff(f457,plain,
( ( h($false) != h($false) )
| ~ spl6_14
| ~ spl6_19
| spl6_26 ),
inference(forward_demodulation,[],[f455,f438]) ).
tff(f438,plain,
( ( $false = bG3 )
| ~ spl6_14
| ~ spl6_19 ),
inference(trivial_inequality_removal,[],[f234]) ).
tff(f234,plain,
( ( $true = $false )
| ( $false = bG3 )
| ~ spl6_14
| ~ spl6_19 ),
inference(superposition,[],[f153,f94]) ).
tff(f153,plain,
( ( $false = bG3 )
| ~ spl6_19 ),
inference(avatar_component_clause,[],[f151]) ).
tff(f455,plain,
( ( h(bG3) != h($false) )
| spl6_26 ),
inference(avatar_component_clause,[],[f453]) ).
tff(f456,plain,
( ~ spl6_26
| spl6_1
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f399,f117,f33,f453]) ).
tff(f399,plain,
( ( h(bG3) != h($false) )
| spl6_1
| ~ spl6_15 ),
inference(superposition,[],[f35,f119]) ).
tff(f119,plain,
( ( $false = bG5 )
| ~ spl6_15 ),
inference(avatar_component_clause,[],[f117]) ).
tff(f451,plain,
( ~ spl6_9
| spl6_8 ),
inference(avatar_split_clause,[],[f24,f66,f70]) ).
tff(f24,plain,
( f(bG2)
| ( $true != bG3 ) ),
inference(cnf_transformation,[],[f15]) ).
tff(f15,plain,
( ( f(bG2)
| ( $true != bG3 ) )
& ( ( $true = bG3 )
| ~ f(bG2) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f8,plain,
( f(bG2)
<=> ( $true = bG3 ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG3])]) ).
tff(f434,plain,
( spl6_16
| ~ spl6_10
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f424,f174,f75,f126]) ).
tff(f424,plain,
( f($false)
| ~ spl6_10
| ~ spl6_21 ),
inference(forward_demodulation,[],[f76,f176]) ).
tff(f423,plain,
( ~ spl6_11
| ~ spl6_20 ),
inference(avatar_contradiction_clause,[],[f422]) ).
tff(f422,plain,
( $false
| ~ spl6_11
| ~ spl6_20 ),
inference(trivial_inequality_removal,[],[f421]) ).
tff(f421,plain,
( ( $true = $false )
| ~ spl6_11
| ~ spl6_20 ),
inference(forward_demodulation,[],[f81,f160]) ).
tff(f160,plain,
( ( $false = bG2 )
| ~ spl6_20 ),
inference(avatar_component_clause,[],[f158]) ).
tff(f158,plain,
( spl6_20
<=> ( $false = bG2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_20])]) ).
tff(f412,plain,
( ~ spl6_16
| spl6_12
| ~ spl6_23 ),
inference(avatar_split_clause,[],[f243,f226,f84,f126]) ).
tff(f243,plain,
( ~ f($false)
| spl6_12
| ~ spl6_23 ),
inference(superposition,[],[f86,f228]) ).
tff(f86,plain,
( ~ f(bG0)
| spl6_12 ),
inference(avatar_component_clause,[],[f84]) ).
tff(f395,plain,
( spl6_15
| spl6_1
| ~ spl6_9
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f378,f93,f70,f33,f117]) ).
tff(f378,plain,
( ( $false = bG5 )
| spl6_1
| ~ spl6_9
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f377]) ).
tff(f377,plain,
( ( h($true) != h($true) )
| ( $false = bG5 )
| spl6_1
| ~ spl6_9
| ~ spl6_14 ),
inference(forward_demodulation,[],[f108,f72]) ).
tff(f381,plain,
( spl6_1
| ~ spl6_7
| ~ spl6_9 ),
inference(avatar_contradiction_clause,[],[f380]) ).
tff(f380,plain,
( $false
| spl6_1
| ~ spl6_7
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f379]) ).
tff(f379,plain,
( ( h($true) != h($true) )
| spl6_1
| ~ spl6_7
| ~ spl6_9 ),
inference(forward_demodulation,[],[f123,f72]) ).
tff(f123,plain,
( ( h(bG3) != h($true) )
| spl6_1
| ~ spl6_7 ),
inference(superposition,[],[f35,f63]) ).
tff(f376,plain,
( spl6_1
| ~ spl6_7
| ~ spl6_9 ),
inference(avatar_contradiction_clause,[],[f375]) ).
tff(f375,plain,
( $false
| spl6_1
| ~ spl6_7
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f374]) ).
tff(f374,plain,
( ( h($true) != h($true) )
| spl6_1
| ~ spl6_7
| ~ spl6_9 ),
inference(forward_demodulation,[],[f196,f72]) ).
tff(f196,plain,
( ( h(bG3) != h($true) )
| spl6_1
| ~ spl6_7 ),
inference(superposition,[],[f35,f63]) ).
tff(f368,plain,
( ~ spl6_9
| ~ spl6_19 ),
inference(avatar_contradiction_clause,[],[f367]) ).
tff(f367,plain,
( $false
| ~ spl6_9
| ~ spl6_19 ),
inference(trivial_inequality_removal,[],[f366]) ).
tff(f366,plain,
( ( $true = $false )
| ~ spl6_9
| ~ spl6_19 ),
inference(forward_demodulation,[],[f72,f153]) ).
tff(f360,plain,
( ~ spl6_16
| spl6_8
| ~ spl6_20 ),
inference(avatar_split_clause,[],[f237,f158,f66,f126]) ).
tff(f237,plain,
( ~ f($false)
| spl6_8
| ~ spl6_20 ),
inference(superposition,[],[f68,f160]) ).
tff(f354,plain,
( spl6_25
| ~ spl6_14
| spl6_22 ),
inference(avatar_split_clause,[],[f203,f199,f93,f352]) ).
tff(f199,plain,
( spl6_22
<=> ( h($true) = h($false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_22])]) ).
tff(f203,plain,
( ! [X0: $o] :
( ( h($false) != h((X0)) )
| ( $false = (X0) ) )
| ~ spl6_14
| spl6_22 ),
inference(superposition,[],[f201,f94]) ).
tff(f201,plain,
( ( h($true) != h($false) )
| spl6_22 ),
inference(avatar_component_clause,[],[f199]) ).
tff(f248,plain,
( spl6_24
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f96,f93,f246]) ).
tff(f246,plain,
( spl6_24
<=> ! [X0: $o,X1: $o] :
( ( (X0) = (X1) )
| ( $false = (X1) )
| ( $false = (X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_24])]) ).
tff(f96,plain,
( ! [X0: $o,X1: $o] :
( ( (X0) = (X1) )
| ( $false = (X1) )
| ( $false = (X0) ) )
| ~ spl6_14 ),
inference(superposition,[],[f94,f94]) ).
tff(f229,plain,
( spl6_23
| spl6_5
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f115,f93,f52,f226]) ).
tff(f115,plain,
( ( $false = bG0 )
| spl6_5
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f99]) ).
tff(f99,plain,
( ( $true != $true )
| ( $false = bG0 )
| spl6_5
| ~ spl6_14 ),
inference(superposition,[],[f54,f94]) ).
tff(f54,plain,
( ( $true != bG0 )
| spl6_5 ),
inference(avatar_component_clause,[],[f52]) ).
tff(f219,plain,
( spl6_12
| ~ spl6_13 ),
inference(avatar_split_clause,[],[f213,f88,f84]) ).
tff(f217,plain,
( spl6_6
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f209,f61,f57]) ).
tff(f216,plain,
( ~ spl6_3
| spl6_5
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f141,f93,f52,f43]) ).
tff(f141,plain,
( ~ x
| spl6_5
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f140]) ).
tff(f140,plain,
( ( $true = $false )
| ~ x
| spl6_5
| ~ spl6_14 ),
inference(forward_demodulation,[],[f29,f115]) ).
tff(f204,plain,
( ~ spl6_18
| ~ spl6_5
| spl6_12 ),
inference(avatar_split_clause,[],[f143,f84,f52,f145]) ).
tff(f143,plain,
( ~ f($true)
| ~ spl6_5
| spl6_12 ),
inference(superposition,[],[f86,f53]) ).
tff(f202,plain,
( ~ spl6_22
| spl6_1
| ~ spl6_7
| spl6_9
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f124,f93,f70,f61,f33,f199]) ).
tff(f124,plain,
( ( h($true) != h($false) )
| spl6_1
| ~ spl6_7
| spl6_9
| ~ spl6_14 ),
inference(forward_demodulation,[],[f123,f112]) ).
tff(f112,plain,
( ( $false = bG3 )
| spl6_9
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f104]) ).
tff(f104,plain,
( ( $true != $true )
| ( $false = bG3 )
| spl6_9
| ~ spl6_14 ),
inference(superposition,[],[f71,f94]) ).
tff(f71,plain,
( ( $true != bG3 )
| spl6_9 ),
inference(avatar_component_clause,[],[f70]) ).
tff(f192,plain,
( ~ spl6_7
| ~ spl6_15 ),
inference(avatar_contradiction_clause,[],[f191]) ).
tff(f191,plain,
( $false
| ~ spl6_7
| ~ spl6_15 ),
inference(trivial_inequality_removal,[],[f190]) ).
tff(f190,plain,
( ( $true = $false )
| ~ spl6_7
| ~ spl6_15 ),
inference(forward_demodulation,[],[f63,f119]) ).
tff(f188,plain,
( ~ spl6_13
| spl6_18
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f180,f52,f145,f88]) ).
tff(f180,plain,
( f($true)
| ( $true != bG1 )
| ~ spl6_5 ),
inference(forward_demodulation,[],[f28,f53]) ).
tff(f181,plain,
( spl6_10
| ~ spl6_11 ),
inference(avatar_split_clause,[],[f179,f79,f75]) ).
tff(f179,plain,
( f(bG1)
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f178]) ).
tff(f178,plain,
( ( $true != $true )
| f(bG1)
| ~ spl6_11 ),
inference(forward_demodulation,[],[f26,f81]) ).
tff(f26,plain,
( f(bG1)
| ( $true != bG2 ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f16,plain,
( ( f(bG1)
| ( $true != bG2 ) )
& ( ( $true = bG2 )
| ~ f(bG1) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f7,plain,
( f(bG1)
<=> ( $true = bG2 ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG2])]) ).
tff(f177,plain,
( spl6_21
| spl6_13
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f114,f93,f88,f174]) ).
tff(f114,plain,
( ( $false = bG1 )
| spl6_13
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f100]) ).
tff(f100,plain,
( ( $true != $true )
| ( $false = bG1 )
| spl6_13
| ~ spl6_14 ),
inference(superposition,[],[f89,f94]) ).
tff(f89,plain,
( ( $true != bG1 )
| spl6_13 ),
inference(avatar_component_clause,[],[f88]) ).
tff(f172,plain,
( ~ spl6_9
| spl6_18
| ~ spl6_11 ),
inference(avatar_split_clause,[],[f169,f79,f145,f70]) ).
tff(f169,plain,
( f($true)
| ( $true != bG3 )
| ~ spl6_11 ),
inference(forward_demodulation,[],[f24,f81]) ).
tff(f167,plain,
( spl6_18
| ~ spl6_8
| ~ spl6_11 ),
inference(avatar_split_clause,[],[f166,f79,f66,f145]) ).
tff(f166,plain,
( f($true)
| ~ spl6_8
| ~ spl6_11 ),
inference(forward_demodulation,[],[f67,f81]) ).
tff(f67,plain,
( f(bG2)
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f66]) ).
tff(f165,plain,
( spl6_8
| ~ spl6_9 ),
inference(avatar_split_clause,[],[f163,f70,f66]) ).
tff(f163,plain,
( f(bG2)
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f162]) ).
tff(f162,plain,
( ( $true != $true )
| f(bG2)
| ~ spl6_9 ),
inference(forward_demodulation,[],[f24,f72]) ).
tff(f161,plain,
( spl6_20
| spl6_11
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f113,f93,f79,f158]) ).
tff(f113,plain,
( ( $false = bG2 )
| spl6_11
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f102]) ).
tff(f102,plain,
( ( $true != $true )
| ( $false = bG2 )
| spl6_11
| ~ spl6_14 ),
inference(superposition,[],[f80,f94]) ).
tff(f80,plain,
( ( $true != bG2 )
| spl6_11 ),
inference(avatar_component_clause,[],[f79]) ).
tff(f156,plain,
( ~ spl6_9
| spl6_16
| spl6_11
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f155,f93,f79,f126,f70]) ).
tff(f155,plain,
( f($false)
| ( $true != bG3 )
| spl6_11
| ~ spl6_14 ),
inference(forward_demodulation,[],[f24,f113]) ).
tff(f154,plain,
( spl6_19
| spl6_9
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f112,f93,f70,f151]) ).
tff(f148,plain,
( ~ spl6_18
| ~ spl6_4
| spl6_6 ),
inference(avatar_split_clause,[],[f138,f57,f47,f145]) ).
tff(f138,plain,
( ~ f($true)
| ~ spl6_4
| spl6_6 ),
inference(superposition,[],[f59,f49]) ).
tff(f142,plain,
( ~ spl6_3
| spl6_5
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f141,f93,f52,f43]) ).
tff(f139,plain,
( ~ spl6_4
| spl6_3 ),
inference(avatar_split_clause,[],[f22,f43,f47]) ).
tff(f22,plain,
( x
| ( $true != bG4 ) ),
inference(cnf_transformation,[],[f14]) ).
tff(f14,plain,
( ( x
| ( $true != bG4 ) )
& ( ( $true = bG4 )
| ~ x ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f9,plain,
( x
<=> ( $true = bG4 ) ),
introduced(fool_formula_definition,[new_symbols(definition,[bG4])]) ).
tff(f136,plain,
( spl6_17
| spl6_4
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f111,f93,f47,f133]) ).
tff(f111,plain,
( ( $false = bG4 )
| spl6_4
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f106]) ).
tff(f106,plain,
( ( $true != $true )
| ( $false = bG4 )
| spl6_4
| ~ spl6_14 ),
inference(superposition,[],[f48,f94]) ).
tff(f48,plain,
( ( $true != bG4 )
| spl6_4 ),
inference(avatar_component_clause,[],[f47]) ).
tff(f129,plain,
( ~ spl6_7
| spl6_16
| spl6_4
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f122,f93,f47,f126,f61]) ).
tff(f122,plain,
( f($false)
| ( $true != bG5 )
| spl6_4
| ~ spl6_14 ),
inference(forward_demodulation,[],[f20,f111]) ).
tff(f120,plain,
( spl6_15
| spl6_7
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f110,f93,f61,f117]) ).
tff(f110,plain,
( ( $false = bG5 )
| spl6_7
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f107]) ).
tff(f107,plain,
( ( $true != $true )
| ( $false = bG5 )
| spl6_7
| ~ spl6_14 ),
inference(superposition,[],[f62,f94]) ).
tff(f62,plain,
( ( $true != bG5 )
| spl6_7 ),
inference(avatar_component_clause,[],[f61]) ).
tff(f95,plain,
spl6_14,
inference(avatar_split_clause,[],[f4,f93]) ).
tff(f4,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(fool_axiom,[]) ).
tff(f91,plain,
( ~ spl6_12
| spl6_13 ),
inference(avatar_split_clause,[],[f27,f88,f84]) ).
tff(f27,plain,
( ( $true = bG1 )
| ~ f(bG0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f82,plain,
( ~ spl6_10
| spl6_11 ),
inference(avatar_split_clause,[],[f25,f79,f75]) ).
tff(f25,plain,
( ( $true = bG2 )
| ~ f(bG1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f73,plain,
( ~ spl6_8
| spl6_9 ),
inference(avatar_split_clause,[],[f23,f70,f66]) ).
tff(f23,plain,
( ( $true = bG3 )
| ~ f(bG2) ),
inference(cnf_transformation,[],[f15]) ).
tff(f64,plain,
( ~ spl6_6
| spl6_7 ),
inference(avatar_split_clause,[],[f19,f61,f57]) ).
tff(f19,plain,
( ( $true = bG5 )
| ~ f(bG4) ),
inference(cnf_transformation,[],[f13]) ).
tff(f55,plain,
( ~ spl6_5
| spl6_3 ),
inference(avatar_split_clause,[],[f30,f43,f52]) ).
tff(f30,plain,
( x
| ( $true != bG0 ) ),
inference(cnf_transformation,[],[f18]) ).
tff(f50,plain,
( ~ spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f21,f47,f43]) ).
tff(f21,plain,
( ( $true = bG4 )
| ~ x ),
inference(cnf_transformation,[],[f14]) ).
tff(f41,plain,
~ spl6_2,
inference(avatar_split_clause,[],[f3,f38]) ).
tff(f38,plain,
( spl6_2
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
tff(f3,plain,
$true != $false,
introduced(fool_axiom,[]) ).
tff(f36,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f31,f33]) ).
tff(f31,plain,
h(bG3) != h(bG5),
inference(cnf_transformation,[],[f12]) ).
tff(f12,plain,
h(bG3) != h(bG5),
inference(flattening,[],[f11]) ).
tff(f11,plain,
( ~ h(bG3) = h(bG5) ),
inference(fool_elimination,[],[f2,f10,f9,f8,f7,f6,f5]) ).
tff(f2,negated_conjecture,
( ~ h(f(f(f(x)))) = h(f(x)) ),
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
h(f(f(f(x)))) = h(f(x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO040_8 : TPTP v8.2.0. Released v8.0.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 20 10:38:08 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % (18742)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36 % (18747)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.36 % (18745)WARNING: value z3 for option sas not known
% 0.12/0.36 % (18748)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.36 % (18749)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.36 % (18746)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.36 % (18744)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.36 % (18743)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.36 % (18745)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.36 Detected minimum model sizes of [1,1]
% 0.12/0.36 Detected maximum model sizes of [max,8]
% 0.12/0.36 TRYING [1,1]
% 0.12/0.36 TRYING [1,2]
% 0.12/0.36 TRYING [1]
% 0.12/0.36 TRYING [2,2]
% 0.12/0.36 TRYING [2]
% 0.12/0.36 TRYING [3,2]
% 0.12/0.36 TRYING [3]
% 0.12/0.36 TRYING [2,3]
% 0.12/0.36 TRYING [3,3]
% 0.12/0.36 TRYING [2,4]
% 0.12/0.36 TRYING [4]
% 0.12/0.36 TRYING [3,4]
% 0.12/0.36 TRYING [2,5]
% 0.12/0.36 TRYING [4,2]
% 0.12/0.36 TRYING [3,5]
% 0.12/0.36 TRYING [5]
% 0.12/0.36 TRYING [2,6]
% 0.12/0.36 TRYING [4,3]
% 0.12/0.37 TRYING [3,6]
% 0.12/0.37 TRYING [2,7]
% 0.12/0.37 TRYING [4,4]
% 0.12/0.37 TRYING [3,7]
% 0.12/0.37 TRYING [6]
% 0.12/0.37 TRYING [2,8]
% 0.12/0.37 TRYING [4,5]
% 0.12/0.37 TRYING [3,8]
% 0.12/0.37 TRYING [4,6]
% 0.12/0.37 TRYING [4,7]
% 0.12/0.37 TRYING [4,8]
% 0.12/0.37 Cannot enumerate next child to try in an incomplete setup
% 0.12/0.37 % (18746)Refutation not found, incomplete strategy% (18746)------------------------------
% 0.12/0.37 % (18746)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.37 % (18746)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.37
% 0.12/0.37 % (18746)Memory used [KB]: 737
% 0.12/0.37 % (18746)Time elapsed: 0.016 s
% 0.12/0.37 % (18746)Instructions burned: 25 (million)
% 0.12/0.37 TRYING [7]
% 0.12/0.37 % (18746)------------------------------
% 0.12/0.37 % (18746)------------------------------
% 0.12/0.37 % (18747)First to succeed.
% 0.12/0.38 % (18747)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18742"
% 0.12/0.38 % (18747)Refutation found. Thanks to Tanya!
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.38 % (18747)------------------------------
% 0.12/0.38 % (18747)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.38 % (18747)Termination reason: Refutation
% 0.12/0.38
% 0.12/0.38 % (18747)Memory used [KB]: 904
% 0.12/0.38 % (18747)Time elapsed: 0.022 s
% 0.12/0.38 % (18747)Instructions burned: 33 (million)
% 0.12/0.38 % (18742)Success in time 0.036 s
%------------------------------------------------------------------------------