TSTP Solution File: SYN015-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYN015-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 08:33:44 EDT 2024
% Result : Unsatisfiable 0.13s 0.40s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 87
% Syntax : Number of formulae : 390 ( 15 unt; 0 def)
% Number of atoms : 1856 ( 687 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 2215 ( 749 ~;1395 |; 0 &)
% ( 71 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 74 ( 72 usr; 72 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 160 ( 160 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1071,plain,
$false,
inference(avatar_sat_refutation,[],[f24,f33,f39,f48,f55,f60,f69,f73,f78,f82,f86,f90,f94,f98,f102,f106,f112,f120,f124,f157,f174,f188,f193,f194,f213,f223,f228,f232,f239,f243,f257,f259,f267,f268,f288,f300,f310,f316,f323,f327,f341,f344,f349,f384,f390,f437,f444,f450,f454,f472,f476,f485,f492,f496,f500,f508,f521,f527,f531,f539,f541,f546,f554,f568,f573,f589,f604,f616,f632,f641,f669,f680,f684,f712,f725,f748,f780,f807,f821,f833,f850,f861,f874,f907,f925,f947,f953,f961,f963,f987,f996,f1005,f1027,f1033,f1048,f1070]) ).
fof(f1070,plain,
( ~ spl0_2
| ~ spl0_7
| spl0_30 ),
inference(avatar_split_clause,[],[f1069,f181,f52,f26]) ).
fof(f26,plain,
( spl0_2
<=> element(k,j) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f52,plain,
( spl0_7
<=> m = j ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f181,plain,
( spl0_30
<=> element(k,m) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1069,plain,
( ~ element(k,j)
| ~ spl0_7
| spl0_30 ),
inference(forward_demodulation,[],[f182,f53]) ).
fof(f53,plain,
( m = j
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f182,plain,
( ~ element(k,m)
| spl0_30 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f1048,plain,
( ~ spl0_10
| ~ spl0_41
| spl0_42 ),
inference(avatar_split_clause,[],[f924,f285,f281,f66]) ).
fof(f66,plain,
( spl0_10
<=> n = k ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f281,plain,
( spl0_41
<=> n = f(k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f285,plain,
( spl0_42
<=> k = f(k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f924,plain,
( n != k
| ~ spl0_41
| spl0_42 ),
inference(superposition,[],[f286,f283]) ).
fof(f283,plain,
( n = f(k)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f286,plain,
( k != f(k)
| spl0_42 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f1033,plain,
( ~ spl0_10
| spl0_63
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f713,f638,f634,f66]) ).
fof(f634,plain,
( spl0_63
<=> n = f(n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f638,plain,
( spl0_64
<=> k = f(n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f713,plain,
( n != k
| spl0_63
| ~ spl0_64 ),
inference(forward_demodulation,[],[f635,f640]) ).
fof(f640,plain,
( k = f(n)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f635,plain,
( n != f(n)
| spl0_63 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f1027,plain,
( spl0_71
| ~ spl0_19
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f795,f339,f104,f1025]) ).
fof(f1025,plain,
( spl0_71
<=> ! [X0] :
( g(X0) = X0
| m = X0
| m = g(X0)
| element(g(X0),m)
| element(X0,n)
| n = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f104,plain,
( spl0_19
<=> ! [X0] :
( n = X0
| element(X0,n)
| element(g(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f339,plain,
( spl0_47
<=> ! [X0] :
( ~ element(g(X0),X0)
| g(X0) = X0
| m = X0
| m = g(X0)
| element(g(X0),m)
| element(X0,n)
| n = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f795,plain,
( ! [X0] :
( g(X0) = X0
| m = X0
| m = g(X0)
| element(g(X0),m)
| element(X0,n)
| n = X0 )
| ~ spl0_19
| ~ spl0_47 ),
inference(duplicate_literal_removal,[],[f785]) ).
fof(f785,plain,
( ! [X0] :
( g(X0) = X0
| m = X0
| m = g(X0)
| element(g(X0),m)
| element(X0,n)
| n = X0
| element(X0,n)
| n = X0 )
| ~ spl0_19
| ~ spl0_47 ),
inference(resolution,[],[f340,f105]) ).
fof(f105,plain,
( ! [X0] :
( element(g(X0),X0)
| element(X0,n)
| n = X0 )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f340,plain,
( ! [X0] :
( ~ element(g(X0),X0)
| g(X0) = X0
| m = X0
| m = g(X0)
| element(g(X0),m)
| element(X0,n)
| n = X0 )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f1005,plain,
( spl0_70
| ~ spl0_7
| ~ spl0_10
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f992,f985,f66,f52,f1003]) ).
fof(f1003,plain,
( spl0_70
<=> ! [X0] :
( k = X0
| element(X0,k)
| element(X0,j)
| j = X0
| j = g(X0)
| g(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f985,plain,
( spl0_68
<=> ! [X0] :
( g(X0) = X0
| m = g(X0)
| m = X0
| element(X0,m)
| element(X0,n)
| n = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f992,plain,
( ! [X0] :
( k = X0
| element(X0,k)
| element(X0,j)
| j = X0
| j = g(X0)
| g(X0) = X0 )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_68 ),
inference(forward_demodulation,[],[f991,f68]) ).
fof(f68,plain,
( n = k
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f991,plain,
( ! [X0] :
( element(X0,k)
| element(X0,j)
| j = X0
| j = g(X0)
| g(X0) = X0
| n = X0 )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_68 ),
inference(forward_demodulation,[],[f990,f68]) ).
fof(f990,plain,
( ! [X0] :
( element(X0,j)
| j = X0
| j = g(X0)
| g(X0) = X0
| element(X0,n)
| n = X0 )
| ~ spl0_7
| ~ spl0_68 ),
inference(forward_demodulation,[],[f989,f53]) ).
fof(f989,plain,
( ! [X0] :
( j = X0
| j = g(X0)
| g(X0) = X0
| element(X0,m)
| element(X0,n)
| n = X0 )
| ~ spl0_7
| ~ spl0_68 ),
inference(forward_demodulation,[],[f988,f53]) ).
fof(f988,plain,
( ! [X0] :
( j = g(X0)
| g(X0) = X0
| m = X0
| element(X0,m)
| element(X0,n)
| n = X0 )
| ~ spl0_7
| ~ spl0_68 ),
inference(forward_demodulation,[],[f986,f53]) ).
fof(f986,plain,
( ! [X0] :
( g(X0) = X0
| m = g(X0)
| m = X0
| element(X0,m)
| element(X0,n)
| n = X0 )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f985]) ).
fof(f996,plain,
( spl0_69
| ~ spl0_14
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f775,f314,f84,f994]) ).
fof(f994,plain,
( spl0_69
<=> ! [X0] :
( ~ element(X0,n)
| f(X0) = X0
| n = f(X0)
| n = X0
| m = X0
| ~ element(X0,m) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f84,plain,
( spl0_14
<=> ! [X0] :
( ~ element(X0,m)
| m = X0
| element(X0,f(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f314,plain,
( spl0_44
<=> ! [X0] :
( ~ element(X0,f(X0))
| ~ element(X0,n)
| f(X0) = X0
| n = f(X0)
| n = X0
| m = X0
| ~ element(X0,m) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f775,plain,
( ! [X0] :
( ~ element(X0,n)
| f(X0) = X0
| n = f(X0)
| n = X0
| m = X0
| ~ element(X0,m) )
| ~ spl0_14
| ~ spl0_44 ),
inference(duplicate_literal_removal,[],[f770]) ).
fof(f770,plain,
( ! [X0] :
( ~ element(X0,n)
| f(X0) = X0
| n = f(X0)
| n = X0
| m = X0
| ~ element(X0,m)
| m = X0
| ~ element(X0,m) )
| ~ spl0_14
| ~ spl0_44 ),
inference(resolution,[],[f315,f85]) ).
fof(f85,plain,
( ! [X0] :
( element(X0,f(X0))
| m = X0
| ~ element(X0,m) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f315,plain,
( ! [X0] :
( ~ element(X0,f(X0))
| ~ element(X0,n)
| f(X0) = X0
| n = f(X0)
| n = X0
| m = X0
| ~ element(X0,m) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f987,plain,
( spl0_68
| ~ spl0_18
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f766,f308,f100,f985]) ).
fof(f100,plain,
( spl0_18
<=> ! [X0] :
( n = X0
| element(X0,n)
| element(X0,g(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f308,plain,
( spl0_43
<=> ! [X0] :
( ~ element(X0,g(X0))
| g(X0) = X0
| m = g(X0)
| m = X0
| element(X0,m)
| element(X0,n)
| n = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f766,plain,
( ! [X0] :
( g(X0) = X0
| m = g(X0)
| m = X0
| element(X0,m)
| element(X0,n)
| n = X0 )
| ~ spl0_18
| ~ spl0_43 ),
inference(duplicate_literal_removal,[],[f764]) ).
fof(f764,plain,
( ! [X0] :
( g(X0) = X0
| m = g(X0)
| m = X0
| element(X0,m)
| element(X0,n)
| n = X0
| element(X0,n)
| n = X0 )
| ~ spl0_18
| ~ spl0_43 ),
inference(resolution,[],[f309,f101]) ).
fof(f101,plain,
( ! [X0] :
( element(X0,g(X0))
| element(X0,n)
| n = X0 )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f309,plain,
( ! [X0] :
( ~ element(X0,g(X0))
| g(X0) = X0
| m = g(X0)
| m = X0
| element(X0,m)
| element(X0,n)
| n = X0 )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f963,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_25 ),
inference(avatar_split_clause,[],[f962,f154,f52,f36]) ).
fof(f36,plain,
( spl0_4
<=> element(j,j) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f154,plain,
( spl0_25
<=> element(j,m) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f962,plain,
( ~ element(j,j)
| ~ spl0_7
| spl0_25 ),
inference(forward_demodulation,[],[f156,f53]) ).
fof(f156,plain,
( ~ element(j,m)
| spl0_25 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f961,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f950,f57,f52,f36]) ).
fof(f57,plain,
( spl0_8
<=> element(m,j) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f950,plain,
( ~ element(j,j)
| ~ spl0_7
| spl0_8 ),
inference(superposition,[],[f58,f53]) ).
fof(f58,plain,
( ~ element(m,j)
| spl0_8 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f953,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f948,f154,f52,f36]) ).
fof(f948,plain,
( element(j,j)
| ~ spl0_7
| ~ spl0_25 ),
inference(superposition,[],[f155,f53]) ).
fof(f155,plain,
( element(j,m)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f947,plain,
( spl0_7
| spl0_28
| spl0_3
| ~ spl0_20
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f933,f190,f110,f30,f167,f52]) ).
fof(f167,plain,
( spl0_28
<=> n = j ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f30,plain,
( spl0_3
<=> j = k ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f110,plain,
( spl0_20
<=> ! [X0] :
( ~ element(X0,k)
| k = X0
| n = X0
| m = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f190,plain,
( spl0_32
<=> element(j,k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f933,plain,
( j = k
| n = j
| m = j
| ~ spl0_20
| ~ spl0_32 ),
inference(resolution,[],[f191,f111]) ).
fof(f111,plain,
( ! [X0] :
( ~ element(X0,k)
| k = X0
| n = X0
| m = X0 )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f191,plain,
( element(j,k)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f925,plain,
( spl0_32
| ~ spl0_10
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f881,f171,f66,f190]) ).
fof(f171,plain,
( spl0_29
<=> element(j,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f881,plain,
( element(j,k)
| ~ spl0_10
| ~ spl0_29 ),
inference(superposition,[],[f173,f68]) ).
fof(f173,plain,
( element(j,n)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f907,plain,
( ~ spl0_2
| ~ spl0_10
| spl0_48 ),
inference(avatar_split_clause,[],[f883,f434,f66,f26]) ).
fof(f434,plain,
( spl0_48
<=> element(n,j) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f883,plain,
( ~ element(k,j)
| ~ spl0_10
| spl0_48 ),
inference(superposition,[],[f435,f68]) ).
fof(f435,plain,
( ~ element(n,j)
| spl0_48 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f874,plain,
( ~ spl0_30
| spl0_6
| ~ spl0_13
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f517,f285,f80,f45,f181]) ).
fof(f45,plain,
( spl0_6
<=> m = k ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f80,plain,
( spl0_13
<=> ! [X0] :
( ~ element(X0,m)
| m = X0
| f(X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f517,plain,
( m = k
| ~ element(k,m)
| ~ spl0_13
| ~ spl0_42 ),
inference(trivial_inequality_removal,[],[f515]) ).
fof(f515,plain,
( k != k
| m = k
| ~ element(k,m)
| ~ spl0_13
| ~ spl0_42 ),
inference(superposition,[],[f81,f287]) ).
fof(f287,plain,
( k = f(k)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f81,plain,
( ! [X0] :
( f(X0) != X0
| m = X0
| ~ element(X0,m) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f861,plain,
( ~ spl0_30
| spl0_6
| spl0_31
| ~ spl0_14
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f855,f281,f84,f185,f45,f181]) ).
fof(f185,plain,
( spl0_31
<=> element(k,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f855,plain,
( element(k,n)
| m = k
| ~ element(k,m)
| ~ spl0_14
| ~ spl0_41 ),
inference(superposition,[],[f85,f283]) ).
fof(f850,plain,
( ~ spl0_30
| spl0_6
| ~ spl0_12
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f293,f277,f76,f45,f181]) ).
fof(f76,plain,
( spl0_12
<=> ! [X0] :
( ~ element(X0,m)
| m = X0
| m != f(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f277,plain,
( spl0_40
<=> m = f(k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f293,plain,
( m = k
| ~ element(k,m)
| ~ spl0_12
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f292]) ).
fof(f292,plain,
( m != m
| m = k
| ~ element(k,m)
| ~ spl0_12
| ~ spl0_40 ),
inference(superposition,[],[f77,f279]) ).
fof(f279,plain,
( m = f(k)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f77,plain,
( ! [X0] :
( m != f(X0)
| m = X0
| ~ element(X0,m) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f833,plain,
( spl0_10
| spl0_31
| spl0_30
| ~ spl0_18
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f825,f202,f100,f181,f185,f66]) ).
fof(f202,plain,
( spl0_33
<=> m = g(k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f825,plain,
( element(k,m)
| element(k,n)
| n = k
| ~ spl0_18
| ~ spl0_33 ),
inference(superposition,[],[f101,f204]) ).
fof(f204,plain,
( m = g(k)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f821,plain,
( spl0_10
| spl0_31
| ~ spl0_16
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f819,f206,f92,f185,f66]) ).
fof(f92,plain,
( spl0_16
<=> ! [X0] :
( n = X0
| element(X0,n)
| n != g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f206,plain,
( spl0_34
<=> n = g(k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f819,plain,
( element(k,n)
| n = k
| ~ spl0_16
| ~ spl0_34 ),
inference(trivial_inequality_removal,[],[f809]) ).
fof(f809,plain,
( n != n
| element(k,n)
| n = k
| ~ spl0_16
| ~ spl0_34 ),
inference(superposition,[],[f93,f208]) ).
fof(f208,plain,
( n = g(k)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f93,plain,
( ! [X0] :
( n != g(X0)
| element(X0,n)
| n = X0 )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f807,plain,
( spl0_10
| spl0_31
| ~ spl0_17
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f275,f210,f96,f185,f66]) ).
fof(f96,plain,
( spl0_17
<=> ! [X0] :
( n = X0
| element(X0,n)
| g(X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f210,plain,
( spl0_35
<=> k = g(k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f275,plain,
( element(k,n)
| n = k
| ~ spl0_17
| ~ spl0_35 ),
inference(trivial_inequality_removal,[],[f273]) ).
fof(f273,plain,
( k != k
| element(k,n)
| n = k
| ~ spl0_17
| ~ spl0_35 ),
inference(superposition,[],[f97,f212]) ).
fof(f212,plain,
( k = g(k)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f97,plain,
( ! [X0] :
( g(X0) != X0
| element(X0,n)
| n = X0 )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f780,plain,
( spl0_6
| ~ spl0_40
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f509,f285,f277,f45]) ).
fof(f509,plain,
( m = k
| ~ spl0_40
| ~ spl0_42 ),
inference(superposition,[],[f287,f279]) ).
fof(f748,plain,
( ~ spl0_2
| spl0_8
| ~ spl0_33
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f746,f210,f202,f57,f26]) ).
fof(f746,plain,
( ~ element(k,j)
| spl0_8
| ~ spl0_33
| ~ spl0_35 ),
inference(forward_demodulation,[],[f58,f540]) ).
fof(f540,plain,
( m = k
| ~ spl0_33
| ~ spl0_35 ),
inference(forward_demodulation,[],[f204,f212]) ).
fof(f725,plain,
( spl0_10
| ~ spl0_9
| ~ spl0_6
| ~ spl0_12
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f724,f638,f76,f45,f62,f66]) ).
fof(f62,plain,
( spl0_9
<=> element(n,k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f724,plain,
( ~ element(n,k)
| n = k
| ~ spl0_6
| ~ spl0_12
| ~ spl0_64 ),
inference(forward_demodulation,[],[f723,f47]) ).
fof(f47,plain,
( m = k
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f723,plain,
( n = k
| ~ element(n,m)
| ~ spl0_6
| ~ spl0_12
| ~ spl0_64 ),
inference(forward_demodulation,[],[f722,f47]) ).
fof(f722,plain,
( m = n
| ~ element(n,m)
| ~ spl0_6
| ~ spl0_12
| ~ spl0_64 ),
inference(trivial_inequality_removal,[],[f721]) ).
fof(f721,plain,
( k != k
| m = n
| ~ element(n,m)
| ~ spl0_6
| ~ spl0_12
| ~ spl0_64 ),
inference(forward_demodulation,[],[f714,f47]) ).
fof(f714,plain,
( m != k
| m = n
| ~ element(n,m)
| ~ spl0_12
| ~ spl0_64 ),
inference(superposition,[],[f77,f640]) ).
fof(f712,plain,
( spl0_10
| ~ spl0_9
| ~ spl0_6
| ~ spl0_13
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f660,f634,f80,f45,f62,f66]) ).
fof(f660,plain,
( ~ element(n,k)
| n = k
| ~ spl0_6
| ~ spl0_13
| ~ spl0_63 ),
inference(forward_demodulation,[],[f659,f47]) ).
fof(f659,plain,
( n = k
| ~ element(n,m)
| ~ spl0_6
| ~ spl0_13
| ~ spl0_63 ),
inference(forward_demodulation,[],[f658,f47]) ).
fof(f658,plain,
( m = n
| ~ element(n,m)
| ~ spl0_13
| ~ spl0_63 ),
inference(trivial_inequality_removal,[],[f652]) ).
fof(f652,plain,
( n != n
| m = n
| ~ element(n,m)
| ~ spl0_13
| ~ spl0_63 ),
inference(superposition,[],[f81,f636]) ).
fof(f636,plain,
( n = f(n)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f684,plain,
( spl0_67
| ~ spl0_19
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f650,f630,f104,f682]) ).
fof(f682,plain,
( spl0_67
<=> ! [X0] :
( element(g(X0),k)
| g(X0) = g(g(X0))
| k = g(X0)
| n = g(X0)
| k = g(g(X0))
| g(X0) = X0
| n = X0
| element(X0,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f630,plain,
( spl0_62
<=> ! [X0] :
( k = g(g(X0))
| element(g(X0),k)
| g(X0) = g(g(X0))
| k = g(X0)
| n = g(X0)
| ~ element(g(X0),X0)
| g(X0) = X0
| n = X0
| element(X0,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f650,plain,
( ! [X0] :
( element(g(X0),k)
| g(X0) = g(g(X0))
| k = g(X0)
| n = g(X0)
| k = g(g(X0))
| g(X0) = X0
| n = X0
| element(X0,n) )
| ~ spl0_19
| ~ spl0_62 ),
inference(duplicate_literal_removal,[],[f642]) ).
fof(f642,plain,
( ! [X0] :
( element(g(X0),k)
| g(X0) = g(g(X0))
| k = g(X0)
| n = g(X0)
| k = g(g(X0))
| g(X0) = X0
| n = X0
| element(X0,n)
| element(X0,n)
| n = X0 )
| ~ spl0_19
| ~ spl0_62 ),
inference(resolution,[],[f631,f105]) ).
fof(f631,plain,
( ! [X0] :
( ~ element(g(X0),X0)
| element(g(X0),k)
| g(X0) = g(g(X0))
| k = g(X0)
| n = g(X0)
| k = g(g(X0))
| g(X0) = X0
| n = X0
| element(X0,n) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f680,plain,
( spl0_66
| ~ spl0_59
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f610,f602,f587,f678]) ).
fof(f678,plain,
( spl0_66
<=> ! [X0] :
( k = f(g(X0))
| k = g(X0)
| g(X0) = f(g(X0))
| n = f(g(X0))
| k = X0
| g(X0) = X0
| element(X0,n)
| n = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f587,plain,
( spl0_59
<=> ! [X0] :
( k = g(X0)
| k = X0
| element(g(X0),k)
| g(X0) = X0
| element(X0,n)
| n = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f602,plain,
( spl0_60
<=> ! [X0] :
( k = f(X0)
| ~ element(X0,k)
| k = X0
| f(X0) = X0
| n = f(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f610,plain,
( ! [X0] :
( k = f(g(X0))
| k = g(X0)
| g(X0) = f(g(X0))
| n = f(g(X0))
| k = X0
| g(X0) = X0
| element(X0,n)
| n = X0 )
| ~ spl0_59
| ~ spl0_60 ),
inference(duplicate_literal_removal,[],[f608]) ).
fof(f608,plain,
( ! [X0] :
( k = f(g(X0))
| k = g(X0)
| g(X0) = f(g(X0))
| n = f(g(X0))
| k = X0
| k = g(X0)
| g(X0) = X0
| element(X0,n)
| n = X0 )
| ~ spl0_59
| ~ spl0_60 ),
inference(resolution,[],[f603,f588]) ).
fof(f588,plain,
( ! [X0] :
( element(g(X0),k)
| k = X0
| k = g(X0)
| g(X0) = X0
| element(X0,n)
| n = X0 )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f603,plain,
( ! [X0] :
( ~ element(X0,k)
| k = f(X0)
| k = X0
| f(X0) = X0
| n = f(X0) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f669,plain,
( spl0_65
| ~ spl0_56
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f611,f602,f552,f667]) ).
fof(f667,plain,
( spl0_65
<=> ! [X0] :
( k = f(f(X0))
| k = f(X0)
| f(X0) = f(f(X0))
| n = f(f(X0))
| ~ element(X0,k)
| k = X0
| f(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f552,plain,
( spl0_56
<=> ! [X0] :
( ~ element(X0,k)
| element(f(X0),k)
| k = f(X0)
| k = X0
| f(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f611,plain,
( ! [X0] :
( k = f(f(X0))
| k = f(X0)
| f(X0) = f(f(X0))
| n = f(f(X0))
| ~ element(X0,k)
| k = X0
| f(X0) = X0 )
| ~ spl0_56
| ~ spl0_60 ),
inference(duplicate_literal_removal,[],[f606]) ).
fof(f606,plain,
( ! [X0] :
( k = f(f(X0))
| k = f(X0)
| f(X0) = f(f(X0))
| n = f(f(X0))
| ~ element(X0,k)
| k = f(X0)
| k = X0
| f(X0) = X0 )
| ~ spl0_56
| ~ spl0_60 ),
inference(resolution,[],[f603,f553]) ).
fof(f553,plain,
( ! [X0] :
( element(f(X0),k)
| ~ element(X0,k)
| k = f(X0)
| k = X0
| f(X0) = X0 )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f641,plain,
( spl0_63
| spl0_10
| spl0_64
| ~ spl0_9
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f612,f602,f62,f638,f66,f634]) ).
fof(f612,plain,
( k = f(n)
| n = k
| n = f(n)
| ~ spl0_9
| ~ spl0_60 ),
inference(duplicate_literal_removal,[],[f605]) ).
fof(f605,plain,
( k = f(n)
| n = k
| n = f(n)
| n = f(n)
| ~ spl0_9
| ~ spl0_60 ),
inference(resolution,[],[f603,f64]) ).
fof(f64,plain,
( element(n,k)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f632,plain,
( spl0_62
| ~ spl0_38
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f581,f571,f230,f630]) ).
fof(f230,plain,
( spl0_38
<=> ! [X0] :
( ~ element(g(X0),X0)
| ~ element(g(X0),n)
| g(X0) = X0
| n = X0
| n = g(X0)
| element(X0,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f571,plain,
( spl0_58
<=> ! [X0] :
( k = X0
| k = g(X0)
| element(X0,k)
| g(X0) = X0
| element(X0,n)
| n = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f581,plain,
( ! [X0] :
( k = g(g(X0))
| element(g(X0),k)
| g(X0) = g(g(X0))
| k = g(X0)
| n = g(X0)
| ~ element(g(X0),X0)
| g(X0) = X0
| n = X0
| element(X0,n) )
| ~ spl0_38
| ~ spl0_58 ),
inference(duplicate_literal_removal,[],[f574]) ).
fof(f574,plain,
( ! [X0] :
( k = g(g(X0))
| element(g(X0),k)
| g(X0) = g(g(X0))
| k = g(X0)
| n = g(X0)
| ~ element(g(X0),X0)
| g(X0) = X0
| n = X0
| n = g(X0)
| element(X0,n) )
| ~ spl0_38
| ~ spl0_58 ),
inference(resolution,[],[f572,f231]) ).
fof(f231,plain,
( ! [X0] :
( ~ element(g(X0),n)
| ~ element(g(X0),X0)
| g(X0) = X0
| n = X0
| n = g(X0)
| element(X0,n) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f572,plain,
( ! [X0] :
( element(X0,n)
| k = g(X0)
| element(X0,k)
| g(X0) = X0
| k = X0
| n = X0 )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f616,plain,
( spl0_61
| ~ spl0_6
| ~ spl0_20
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f600,f587,f110,f45,f614]) ).
fof(f614,plain,
( spl0_61
<=> ! [X0] :
( k = g(X0)
| k = X0
| g(X0) = X0
| element(X0,n)
| n = X0
| n = g(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f600,plain,
( ! [X0] :
( k = g(X0)
| k = X0
| g(X0) = X0
| element(X0,n)
| n = X0
| n = g(X0) )
| ~ spl0_6
| ~ spl0_20
| ~ spl0_59 ),
inference(duplicate_literal_removal,[],[f599]) ).
fof(f599,plain,
( ! [X0] :
( k = g(X0)
| k = X0
| k = g(X0)
| g(X0) = X0
| element(X0,n)
| n = X0
| n = g(X0) )
| ~ spl0_6
| ~ spl0_20
| ~ spl0_59 ),
inference(forward_demodulation,[],[f597,f47]) ).
fof(f597,plain,
( ! [X0] :
( k = X0
| k = g(X0)
| g(X0) = X0
| element(X0,n)
| n = X0
| n = g(X0)
| m = g(X0) )
| ~ spl0_20
| ~ spl0_59 ),
inference(duplicate_literal_removal,[],[f591]) ).
fof(f591,plain,
( ! [X0] :
( k = X0
| k = g(X0)
| g(X0) = X0
| element(X0,n)
| n = X0
| k = g(X0)
| n = g(X0)
| m = g(X0) )
| ~ spl0_20
| ~ spl0_59 ),
inference(resolution,[],[f588,f111]) ).
fof(f604,plain,
( spl0_60
| ~ spl0_6
| ~ spl0_20
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f564,f552,f110,f45,f602]) ).
fof(f564,plain,
( ! [X0] :
( k = f(X0)
| ~ element(X0,k)
| k = X0
| f(X0) = X0
| n = f(X0) )
| ~ spl0_6
| ~ spl0_20
| ~ spl0_56 ),
inference(duplicate_literal_removal,[],[f563]) ).
fof(f563,plain,
( ! [X0] :
( k = f(X0)
| ~ element(X0,k)
| k = f(X0)
| k = X0
| f(X0) = X0
| n = f(X0) )
| ~ spl0_6
| ~ spl0_20
| ~ spl0_56 ),
inference(forward_demodulation,[],[f562,f47]) ).
fof(f562,plain,
( ! [X0] :
( ~ element(X0,k)
| k = f(X0)
| k = X0
| f(X0) = X0
| n = f(X0)
| m = f(X0) )
| ~ spl0_20
| ~ spl0_56 ),
inference(duplicate_literal_removal,[],[f555]) ).
fof(f555,plain,
( ! [X0] :
( ~ element(X0,k)
| k = f(X0)
| k = X0
| f(X0) = X0
| k = f(X0)
| n = f(X0)
| m = f(X0) )
| ~ spl0_20
| ~ spl0_56 ),
inference(resolution,[],[f553,f111]) ).
fof(f589,plain,
( spl0_59
| ~ spl0_19
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f534,f525,f104,f587]) ).
fof(f525,plain,
( spl0_53
<=> ! [X0] :
( element(g(X0),k)
| k = g(X0)
| k = X0
| ~ element(g(X0),X0)
| g(X0) = X0
| element(X0,n)
| n = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f534,plain,
( ! [X0] :
( k = g(X0)
| k = X0
| element(g(X0),k)
| g(X0) = X0
| element(X0,n)
| n = X0 )
| ~ spl0_19
| ~ spl0_53 ),
inference(duplicate_literal_removal,[],[f532]) ).
fof(f532,plain,
( ! [X0] :
( k = g(X0)
| k = X0
| element(g(X0),k)
| g(X0) = X0
| element(X0,n)
| n = X0
| element(X0,n)
| n = X0 )
| ~ spl0_19
| ~ spl0_53 ),
inference(resolution,[],[f526,f105]) ).
fof(f526,plain,
( ! [X0] :
( ~ element(g(X0),X0)
| k = g(X0)
| k = X0
| element(g(X0),k)
| g(X0) = X0
| element(X0,n)
| n = X0 )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f573,plain,
( spl0_58
| ~ spl0_18
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f503,f490,f100,f571]) ).
fof(f490,plain,
( spl0_49
<=> ! [X0] :
( element(X0,k)
| k = X0
| k = g(X0)
| ~ element(X0,g(X0))
| g(X0) = X0
| element(X0,n)
| n = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f503,plain,
( ! [X0] :
( k = X0
| k = g(X0)
| element(X0,k)
| g(X0) = X0
| element(X0,n)
| n = X0 )
| ~ spl0_18
| ~ spl0_49 ),
inference(duplicate_literal_removal,[],[f501]) ).
fof(f501,plain,
( ! [X0] :
( k = X0
| k = g(X0)
| element(X0,k)
| g(X0) = X0
| element(X0,n)
| n = X0
| element(X0,n)
| n = X0 )
| ~ spl0_18
| ~ spl0_49 ),
inference(resolution,[],[f491,f101]) ).
fof(f491,plain,
( ! [X0] :
( ~ element(X0,g(X0))
| k = X0
| k = g(X0)
| element(X0,k)
| g(X0) = X0
| element(X0,n)
| n = X0 )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f568,plain,
( spl0_57
| ~ spl0_14
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f337,f325,f84,f566]) ).
fof(f566,plain,
( spl0_57
<=> ! [X0] :
( j = f(X0)
| ~ element(X0,j)
| j = X0
| f(X0) = X0
| m = X0
| ~ element(X0,m) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f325,plain,
( spl0_46
<=> ! [X0] :
( j = X0
| j = f(X0)
| ~ element(X0,j)
| ~ element(X0,f(X0))
| f(X0) = X0
| m = X0
| ~ element(X0,m) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f337,plain,
( ! [X0] :
( j = f(X0)
| ~ element(X0,j)
| j = X0
| f(X0) = X0
| m = X0
| ~ element(X0,m) )
| ~ spl0_14
| ~ spl0_46 ),
inference(duplicate_literal_removal,[],[f334]) ).
fof(f334,plain,
( ! [X0] :
( j = f(X0)
| ~ element(X0,j)
| j = X0
| f(X0) = X0
| m = X0
| ~ element(X0,m)
| m = X0
| ~ element(X0,m) )
| ~ spl0_14
| ~ spl0_46 ),
inference(resolution,[],[f326,f85]) ).
fof(f326,plain,
( ! [X0] :
( ~ element(X0,f(X0))
| j = f(X0)
| ~ element(X0,j)
| j = X0
| f(X0) = X0
| m = X0
| ~ element(X0,m) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f554,plain,
( spl0_56
| ~ spl0_6
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f550,f544,f45,f552]) ).
fof(f544,plain,
( spl0_55
<=> ! [X0] :
( f(X0) = X0
| m = X0
| m = f(X0)
| element(f(X0),m)
| ~ element(X0,m) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f550,plain,
( ! [X0] :
( ~ element(X0,k)
| element(f(X0),k)
| k = f(X0)
| k = X0
| f(X0) = X0 )
| ~ spl0_6
| ~ spl0_55 ),
inference(forward_demodulation,[],[f549,f47]) ).
fof(f549,plain,
( ! [X0] :
( element(f(X0),k)
| k = f(X0)
| k = X0
| f(X0) = X0
| ~ element(X0,m) )
| ~ spl0_6
| ~ spl0_55 ),
inference(forward_demodulation,[],[f548,f47]) ).
fof(f548,plain,
( ! [X0] :
( k = f(X0)
| k = X0
| f(X0) = X0
| element(f(X0),m)
| ~ element(X0,m) )
| ~ spl0_6
| ~ spl0_55 ),
inference(forward_demodulation,[],[f547,f47]) ).
fof(f547,plain,
( ! [X0] :
( k = X0
| f(X0) = X0
| m = f(X0)
| element(f(X0),m)
| ~ element(X0,m) )
| ~ spl0_6
| ~ spl0_55 ),
inference(forward_demodulation,[],[f545,f47]) ).
fof(f545,plain,
( ! [X0] :
( element(f(X0),m)
| m = X0
| m = f(X0)
| f(X0) = X0
| ~ element(X0,m) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f546,plain,
( spl0_55
| ~ spl0_15
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f238,f226,f88,f544]) ).
fof(f88,plain,
( spl0_15
<=> ! [X0] :
( ~ element(X0,m)
| m = X0
| element(f(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f226,plain,
( spl0_37
<=> ! [X0] :
( ~ element(f(X0),X0)
| f(X0) = X0
| m = X0
| m = f(X0)
| element(f(X0),m)
| ~ element(X0,m) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f238,plain,
( ! [X0] :
( f(X0) = X0
| m = X0
| m = f(X0)
| element(f(X0),m)
| ~ element(X0,m) )
| ~ spl0_15
| ~ spl0_37 ),
inference(duplicate_literal_removal,[],[f237]) ).
fof(f237,plain,
( ! [X0] :
( f(X0) = X0
| m = X0
| m = f(X0)
| element(f(X0),m)
| ~ element(X0,m)
| m = X0
| ~ element(X0,m) )
| ~ spl0_15
| ~ spl0_37 ),
inference(resolution,[],[f227,f89]) ).
fof(f89,plain,
( ! [X0] :
( element(f(X0),X0)
| m = X0
| ~ element(X0,m) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f227,plain,
( ! [X0] :
( ~ element(f(X0),X0)
| f(X0) = X0
| m = X0
| m = f(X0)
| element(f(X0),m)
| ~ element(X0,m) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f541,plain,
( spl0_36
| ~ spl0_6
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f375,f181,f45,f220]) ).
fof(f220,plain,
( spl0_36
<=> element(k,k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f375,plain,
( element(k,k)
| ~ spl0_6
| ~ spl0_30 ),
inference(superposition,[],[f183,f47]) ).
fof(f183,plain,
( element(k,m)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f539,plain,
( ~ spl0_6
| spl0_33
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f270,f210,f202,f45]) ).
fof(f270,plain,
( m != k
| spl0_33
| ~ spl0_35 ),
inference(superposition,[],[f203,f212]) ).
fof(f203,plain,
( m != g(k)
| spl0_33 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f531,plain,
( spl0_54
| ~ spl0_6
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f523,f519,f45,f529]) ).
fof(f529,plain,
( spl0_54
<=> ! [X0] :
( ~ element(X0,k)
| k = X0
| ~ element(f(X0),X0)
| ~ element(f(X0),n)
| f(X0) = X0
| n = X0
| n = f(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f519,plain,
( spl0_52
<=> ! [X0] :
( ~ element(f(X0),X0)
| ~ element(f(X0),n)
| f(X0) = X0
| n = X0
| n = f(X0)
| m = X0
| ~ element(X0,m) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f523,plain,
( ! [X0] :
( ~ element(X0,k)
| k = X0
| ~ element(f(X0),X0)
| ~ element(f(X0),n)
| f(X0) = X0
| n = X0
| n = f(X0) )
| ~ spl0_6
| ~ spl0_52 ),
inference(forward_demodulation,[],[f522,f47]) ).
fof(f522,plain,
( ! [X0] :
( k = X0
| ~ element(f(X0),X0)
| ~ element(f(X0),n)
| f(X0) = X0
| n = X0
| n = f(X0)
| ~ element(X0,m) )
| ~ spl0_6
| ~ spl0_52 ),
inference(forward_demodulation,[],[f520,f47]) ).
fof(f520,plain,
( ! [X0] :
( ~ element(f(X0),n)
| ~ element(f(X0),X0)
| f(X0) = X0
| n = X0
| n = f(X0)
| m = X0
| ~ element(X0,m) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f527,plain,
( spl0_53
| ~ spl0_6
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f466,f339,f45,f525]) ).
fof(f466,plain,
( ! [X0] :
( element(g(X0),k)
| k = g(X0)
| k = X0
| ~ element(g(X0),X0)
| g(X0) = X0
| element(X0,n)
| n = X0 )
| ~ spl0_6
| ~ spl0_47 ),
inference(forward_demodulation,[],[f465,f47]) ).
fof(f465,plain,
( ! [X0] :
( k = g(X0)
| k = X0
| ~ element(g(X0),X0)
| g(X0) = X0
| element(g(X0),m)
| element(X0,n)
| n = X0 )
| ~ spl0_6
| ~ spl0_47 ),
inference(forward_demodulation,[],[f399,f47]) ).
fof(f399,plain,
( ! [X0] :
( k = X0
| ~ element(g(X0),X0)
| g(X0) = X0
| m = g(X0)
| element(g(X0),m)
| element(X0,n)
| n = X0 )
| ~ spl0_6
| ~ spl0_47 ),
inference(forward_demodulation,[],[f340,f47]) ).
fof(f521,plain,
( spl0_52
| ~ spl0_14
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f135,f122,f84,f519]) ).
fof(f122,plain,
( spl0_22
<=> ! [X2,X0] :
( ~ element(X2,X0)
| ~ element(X0,X2)
| ~ element(X0,n)
| X0 = X2
| n = X2
| n = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f135,plain,
( ! [X0] :
( ~ element(f(X0),X0)
| ~ element(f(X0),n)
| f(X0) = X0
| n = X0
| n = f(X0)
| m = X0
| ~ element(X0,m) )
| ~ spl0_14
| ~ spl0_22 ),
inference(resolution,[],[f123,f85]) ).
fof(f123,plain,
( ! [X2,X0] :
( ~ element(X2,X0)
| ~ element(X0,X2)
| ~ element(X0,n)
| X0 = X2
| n = X2
| n = X0 )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f508,plain,
( ~ spl0_6
| ~ spl0_40
| spl0_42 ),
inference(avatar_split_clause,[],[f295,f285,f277,f45]) ).
fof(f295,plain,
( m != k
| ~ spl0_40
| spl0_42 ),
inference(superposition,[],[f286,f279]) ).
fof(f500,plain,
( spl0_51
| ~ spl0_6
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f464,f321,f45,f498]) ).
fof(f498,plain,
( spl0_51
<=> ! [X0] :
( element(X0,k)
| k = X0
| k = g(X0)
| ~ element(X0,g(X0))
| element(X0,j)
| j = X0
| g(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f321,plain,
( spl0_45
<=> ! [X0] :
( j = X0
| element(X0,j)
| ~ element(X0,g(X0))
| g(X0) = X0
| m = g(X0)
| m = X0
| element(X0,m) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f464,plain,
( ! [X0] :
( element(X0,k)
| k = X0
| k = g(X0)
| ~ element(X0,g(X0))
| element(X0,j)
| j = X0
| g(X0) = X0 )
| ~ spl0_6
| ~ spl0_45 ),
inference(forward_demodulation,[],[f463,f47]) ).
fof(f463,plain,
( ! [X0] :
( k = X0
| k = g(X0)
| ~ element(X0,g(X0))
| element(X0,j)
| j = X0
| g(X0) = X0
| element(X0,m) )
| ~ spl0_6
| ~ spl0_45 ),
inference(forward_demodulation,[],[f405,f47]) ).
fof(f405,plain,
( ! [X0] :
( k = g(X0)
| ~ element(X0,g(X0))
| element(X0,j)
| j = X0
| g(X0) = X0
| m = X0
| element(X0,m) )
| ~ spl0_6
| ~ spl0_45 ),
inference(forward_demodulation,[],[f322,f47]) ).
fof(f322,plain,
( ! [X0] :
( ~ element(X0,g(X0))
| element(X0,j)
| j = X0
| g(X0) = X0
| m = g(X0)
| m = X0
| element(X0,m) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f496,plain,
( spl0_50
| ~ spl0_6
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f460,f314,f45,f494]) ).
fof(f494,plain,
( spl0_50
<=> ! [X0] :
( ~ element(X0,k)
| k = X0
| ~ element(X0,f(X0))
| ~ element(X0,n)
| f(X0) = X0
| n = f(X0)
| n = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f460,plain,
( ! [X0] :
( ~ element(X0,k)
| k = X0
| ~ element(X0,f(X0))
| ~ element(X0,n)
| f(X0) = X0
| n = f(X0)
| n = X0 )
| ~ spl0_6
| ~ spl0_44 ),
inference(forward_demodulation,[],[f421,f47]) ).
fof(f421,plain,
( ! [X0] :
( k = X0
| ~ element(X0,f(X0))
| ~ element(X0,n)
| f(X0) = X0
| n = f(X0)
| n = X0
| ~ element(X0,m) )
| ~ spl0_6
| ~ spl0_44 ),
inference(forward_demodulation,[],[f315,f47]) ).
fof(f492,plain,
( spl0_49
| ~ spl0_6
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f459,f308,f45,f490]) ).
fof(f459,plain,
( ! [X0] :
( element(X0,k)
| k = X0
| k = g(X0)
| ~ element(X0,g(X0))
| g(X0) = X0
| element(X0,n)
| n = X0 )
| ~ spl0_6
| ~ spl0_43 ),
inference(forward_demodulation,[],[f458,f47]) ).
fof(f458,plain,
( ! [X0] :
( k = X0
| k = g(X0)
| ~ element(X0,g(X0))
| g(X0) = X0
| element(X0,m)
| element(X0,n)
| n = X0 )
| ~ spl0_6
| ~ spl0_43 ),
inference(forward_demodulation,[],[f425,f47]) ).
fof(f425,plain,
( ! [X0] :
( k = g(X0)
| ~ element(X0,g(X0))
| g(X0) = X0
| m = X0
| element(X0,m)
| element(X0,n)
| n = X0 )
| ~ spl0_6
| ~ spl0_43 ),
inference(forward_demodulation,[],[f309,f47]) ).
fof(f485,plain,
( spl0_10
| spl0_28
| ~ spl0_11
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f438,f434,f71,f167,f66]) ).
fof(f71,plain,
( spl0_11
<=> ! [X0] :
( ~ element(X0,j)
| j = X0
| k = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f438,plain,
( n = j
| n = k
| ~ spl0_11
| ~ spl0_48 ),
inference(resolution,[],[f436,f72]) ).
fof(f72,plain,
( ! [X0] :
( ~ element(X0,j)
| j = X0
| k = X0 )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f436,plain,
( element(n,j)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f476,plain,
( ~ spl0_36
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f467,f45,f41,f220]) ).
fof(f41,plain,
( spl0_5
<=> element(m,k) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f467,plain,
( ~ element(k,k)
| spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f42,f47]) ).
fof(f42,plain,
( ~ element(m,k)
| spl0_5 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f472,plain,
( spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f258,f57,f45,f26]) ).
fof(f258,plain,
( element(k,j)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f59,f47]) ).
fof(f59,plain,
( element(m,j)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f454,plain,
( ~ spl0_3
| ~ spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f377,f52,f45,f30]) ).
fof(f377,plain,
( j != k
| ~ spl0_6
| spl0_7 ),
inference(superposition,[],[f54,f47]) ).
fof(f54,plain,
( m != j
| spl0_7 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f450,plain,
( ~ spl0_4
| ~ spl0_3
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f389,f45,f41,f30,f36]) ).
fof(f389,plain,
( ~ element(j,j)
| ~ spl0_3
| spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f388,f32]) ).
fof(f32,plain,
( j = k
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f388,plain,
( ~ element(k,j)
| ~ spl0_3
| spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f387,f47]) ).
fof(f387,plain,
( ~ element(m,j)
| ~ spl0_3
| spl0_5 ),
inference(forward_demodulation,[],[f42,f32]) ).
fof(f444,plain,
( spl0_4
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f354,f30,f26,f36]) ).
fof(f354,plain,
( element(j,j)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f28,f32]) ).
fof(f28,plain,
( element(k,j)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f437,plain,
( spl0_48
| ~ spl0_3
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f432,f62,f30,f434]) ).
fof(f432,plain,
( element(n,j)
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f64,f32]) ).
fof(f390,plain,
( ~ spl0_6
| spl0_1
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f218,f66,f21,f45]) ).
fof(f21,plain,
( spl0_1
<=> m = n ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f218,plain,
( m != k
| spl0_1
| ~ spl0_10 ),
inference(superposition,[],[f23,f68]) ).
fof(f23,plain,
( m != n
| spl0_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f384,plain,
( ~ spl0_36
| spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f224,f66,f62,f220]) ).
fof(f224,plain,
( ~ element(k,k)
| spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f63,f68]) ).
fof(f63,plain,
( ~ element(n,k)
| spl0_9 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f349,plain,
( spl0_3
| ~ spl0_10
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f346,f167,f66,f30]) ).
fof(f346,plain,
( j = k
| ~ spl0_10
| ~ spl0_28 ),
inference(forward_demodulation,[],[f68,f169]) ).
fof(f169,plain,
( n = j
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f344,plain,
( spl0_32
| ~ spl0_9
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f302,f167,f62,f190]) ).
fof(f302,plain,
( element(j,k)
| ~ spl0_9
| ~ spl0_28 ),
inference(superposition,[],[f64,f169]) ).
fof(f341,plain,
( spl0_47
| ~ spl0_18
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f126,f118,f100,f339]) ).
fof(f118,plain,
( spl0_21
<=> ! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X0 = X1
| m = X1
| m = X0
| element(X0,m) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f126,plain,
( ! [X0] :
( ~ element(g(X0),X0)
| g(X0) = X0
| m = X0
| m = g(X0)
| element(g(X0),m)
| element(X0,n)
| n = X0 )
| ~ spl0_18
| ~ spl0_21 ),
inference(resolution,[],[f119,f101]) ).
fof(f119,plain,
( ! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X0 = X1
| m = X1
| m = X0
| element(X0,m) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f327,plain,
( spl0_46
| ~ spl0_28
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f319,f314,f167,f325]) ).
fof(f319,plain,
( ! [X0] :
( j = X0
| j = f(X0)
| ~ element(X0,j)
| ~ element(X0,f(X0))
| f(X0) = X0
| m = X0
| ~ element(X0,m) )
| ~ spl0_28
| ~ spl0_44 ),
inference(forward_demodulation,[],[f318,f169]) ).
fof(f318,plain,
( ! [X0] :
( j = f(X0)
| ~ element(X0,j)
| ~ element(X0,f(X0))
| f(X0) = X0
| n = X0
| m = X0
| ~ element(X0,m) )
| ~ spl0_28
| ~ spl0_44 ),
inference(forward_demodulation,[],[f317,f169]) ).
fof(f317,plain,
( ! [X0] :
( ~ element(X0,j)
| ~ element(X0,f(X0))
| f(X0) = X0
| n = f(X0)
| n = X0
| m = X0
| ~ element(X0,m) )
| ~ spl0_28
| ~ spl0_44 ),
inference(forward_demodulation,[],[f315,f169]) ).
fof(f323,plain,
( spl0_45
| ~ spl0_28
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f312,f308,f167,f321]) ).
fof(f312,plain,
( ! [X0] :
( j = X0
| element(X0,j)
| ~ element(X0,g(X0))
| g(X0) = X0
| m = g(X0)
| m = X0
| element(X0,m) )
| ~ spl0_28
| ~ spl0_43 ),
inference(forward_demodulation,[],[f311,f169]) ).
fof(f311,plain,
( ! [X0] :
( element(X0,j)
| ~ element(X0,g(X0))
| g(X0) = X0
| m = g(X0)
| m = X0
| element(X0,m)
| n = X0 )
| ~ spl0_28
| ~ spl0_43 ),
inference(forward_demodulation,[],[f309,f169]) ).
fof(f316,plain,
( spl0_44
| ~ spl0_15
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f140,f122,f88,f314]) ).
fof(f140,plain,
( ! [X0] :
( ~ element(X0,f(X0))
| ~ element(X0,n)
| f(X0) = X0
| n = f(X0)
| n = X0
| m = X0
| ~ element(X0,m) )
| ~ spl0_15
| ~ spl0_22 ),
inference(resolution,[],[f123,f89]) ).
fof(f310,plain,
( spl0_43
| ~ spl0_19
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f131,f118,f104,f308]) ).
fof(f131,plain,
( ! [X0] :
( ~ element(X0,g(X0))
| g(X0) = X0
| m = g(X0)
| m = X0
| element(X0,m)
| element(X0,n)
| n = X0 )
| ~ spl0_19
| ~ spl0_21 ),
inference(resolution,[],[f119,f105]) ).
fof(f300,plain,
( spl0_28
| spl0_29
| ~ spl0_17
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f200,f163,f96,f171,f167]) ).
fof(f163,plain,
( spl0_27
<=> j = g(j) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f200,plain,
( element(j,n)
| n = j
| ~ spl0_17
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f198]) ).
fof(f198,plain,
( j != j
| element(j,n)
| n = j
| ~ spl0_17
| ~ spl0_27 ),
inference(superposition,[],[f97,f165]) ).
fof(f165,plain,
( j = g(j)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f288,plain,
( ~ spl0_30
| spl0_6
| spl0_40
| spl0_41
| spl0_42
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f115,f110,f88,f285,f281,f277,f45,f181]) ).
fof(f115,plain,
( k = f(k)
| n = f(k)
| m = f(k)
| m = k
| ~ element(k,m)
| ~ spl0_15
| ~ spl0_20 ),
inference(resolution,[],[f111,f89]) ).
fof(f268,plain,
( spl0_10
| spl0_1
| spl0_6
| ~ spl0_31
| ~ spl0_30
| ~ spl0_5
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f137,f122,f41,f181,f185,f45,f21,f66]) ).
fof(f137,plain,
( ~ element(k,m)
| ~ element(k,n)
| m = k
| m = n
| n = k
| ~ spl0_5
| ~ spl0_22 ),
inference(resolution,[],[f123,f43]) ).
fof(f43,plain,
( element(m,k)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f267,plain,
( spl0_6
| spl0_7
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f260,f71,f57,f52,f45]) ).
fof(f260,plain,
( m = j
| m = k
| ~ spl0_8
| ~ spl0_11 ),
inference(resolution,[],[f59,f72]) ).
fof(f259,plain,
( spl0_36
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f249,f45,f41,f220]) ).
fof(f249,plain,
( element(k,k)
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f43,f47]) ).
fof(f257,plain,
( ~ spl0_2
| ~ spl0_6
| spl0_8 ),
inference(avatar_split_clause,[],[f247,f57,f45,f26]) ).
fof(f247,plain,
( ~ element(k,j)
| ~ spl0_6
| spl0_8 ),
inference(superposition,[],[f58,f47]) ).
fof(f243,plain,
( spl0_39
| ~ spl0_10
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f236,f230,f66,f241]) ).
fof(f241,plain,
( spl0_39
<=> ! [X0] :
( element(X0,k)
| k = g(X0)
| k = X0
| ~ element(g(X0),k)
| ~ element(g(X0),X0)
| g(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f236,plain,
( ! [X0] :
( element(X0,k)
| k = g(X0)
| k = X0
| ~ element(g(X0),k)
| ~ element(g(X0),X0)
| g(X0) = X0 )
| ~ spl0_10
| ~ spl0_38 ),
inference(forward_demodulation,[],[f235,f68]) ).
fof(f235,plain,
( ! [X0] :
( k = g(X0)
| k = X0
| ~ element(g(X0),k)
| ~ element(g(X0),X0)
| g(X0) = X0
| element(X0,n) )
| ~ spl0_10
| ~ spl0_38 ),
inference(forward_demodulation,[],[f234,f68]) ).
fof(f234,plain,
( ! [X0] :
( k = X0
| ~ element(g(X0),k)
| ~ element(g(X0),X0)
| g(X0) = X0
| n = g(X0)
| element(X0,n) )
| ~ spl0_10
| ~ spl0_38 ),
inference(forward_demodulation,[],[f233,f68]) ).
fof(f233,plain,
( ! [X0] :
( ~ element(g(X0),k)
| ~ element(g(X0),X0)
| g(X0) = X0
| n = X0
| n = g(X0)
| element(X0,n) )
| ~ spl0_10
| ~ spl0_38 ),
inference(forward_demodulation,[],[f231,f68]) ).
fof(f239,plain,
( ~ spl0_36
| ~ spl0_10
| spl0_31 ),
inference(avatar_split_clause,[],[f214,f185,f66,f220]) ).
fof(f214,plain,
( ~ element(k,k)
| ~ spl0_10
| spl0_31 ),
inference(superposition,[],[f187,f68]) ).
fof(f187,plain,
( ~ element(k,n)
| spl0_31 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f232,plain,
( spl0_38
| ~ spl0_18
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f144,f122,f100,f230]) ).
fof(f144,plain,
( ! [X0] :
( ~ element(g(X0),X0)
| ~ element(g(X0),n)
| g(X0) = X0
| n = X0
| n = g(X0)
| element(X0,n) )
| ~ spl0_18
| ~ spl0_22 ),
inference(duplicate_literal_removal,[],[f136]) ).
fof(f136,plain,
( ! [X0] :
( ~ element(g(X0),X0)
| ~ element(g(X0),n)
| g(X0) = X0
| n = X0
| n = g(X0)
| element(X0,n)
| n = X0 )
| ~ spl0_18
| ~ spl0_22 ),
inference(resolution,[],[f123,f101]) ).
fof(f228,plain,
( spl0_37
| ~ spl0_14
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f134,f118,f84,f226]) ).
fof(f134,plain,
( ! [X0] :
( ~ element(f(X0),X0)
| f(X0) = X0
| m = X0
| m = f(X0)
| element(f(X0),m)
| ~ element(X0,m) )
| ~ spl0_14
| ~ spl0_21 ),
inference(duplicate_literal_removal,[],[f125]) ).
fof(f125,plain,
( ! [X0] :
( ~ element(f(X0),X0)
| f(X0) = X0
| m = X0
| m = f(X0)
| element(f(X0),m)
| m = X0
| ~ element(X0,m) )
| ~ spl0_14
| ~ spl0_21 ),
inference(resolution,[],[f119,f85]) ).
fof(f223,plain,
( spl0_36
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f217,f66,f62,f220]) ).
fof(f217,plain,
( element(k,k)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f64,f68]) ).
fof(f213,plain,
( spl0_10
| spl0_31
| spl0_33
| spl0_34
| spl0_35
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f116,f110,f104,f210,f206,f202,f185,f66]) ).
fof(f116,plain,
( k = g(k)
| n = g(k)
| m = g(k)
| element(k,n)
| n = k
| ~ spl0_19
| ~ spl0_20 ),
inference(resolution,[],[f111,f105]) ).
fof(f194,plain,
( spl0_28
| spl0_29
| spl0_32
| ~ spl0_18
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f176,f159,f100,f190,f171,f167]) ).
fof(f159,plain,
( spl0_26
<=> k = g(j) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f176,plain,
( element(j,k)
| element(j,n)
| n = j
| ~ spl0_18
| ~ spl0_26 ),
inference(superposition,[],[f101,f161]) ).
fof(f161,plain,
( k = g(j)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f193,plain,
( spl0_25
| spl0_7
| spl0_6
| spl0_3
| ~ spl0_32
| ~ spl0_2
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f129,f118,f26,f190,f30,f45,f52,f154]) ).
fof(f129,plain,
( ~ element(j,k)
| j = k
| m = k
| m = j
| element(j,m)
| ~ spl0_2
| ~ spl0_21 ),
inference(resolution,[],[f119,f28]) ).
fof(f188,plain,
( spl0_30
| spl0_6
| spl0_1
| spl0_10
| ~ spl0_31
| ~ spl0_9
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f128,f118,f62,f185,f66,f21,f45,f181]) ).
fof(f128,plain,
( ~ element(k,n)
| n = k
| m = n
| m = k
| element(k,m)
| ~ spl0_9
| ~ spl0_21 ),
inference(resolution,[],[f119,f64]) ).
fof(f174,plain,
( spl0_26
| spl0_27
| spl0_28
| spl0_29
| ~ spl0_11
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f108,f104,f71,f171,f167,f163,f159]) ).
fof(f108,plain,
( element(j,n)
| n = j
| j = g(j)
| k = g(j)
| ~ spl0_11
| ~ spl0_19 ),
inference(resolution,[],[f105,f72]) ).
fof(f157,plain,
( spl0_23
| spl0_24
| ~ spl0_25
| spl0_7
| ~ spl0_11
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f107,f88,f71,f52,f154,f150,f146]) ).
fof(f146,plain,
( spl0_23
<=> k = f(j) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f150,plain,
( spl0_24
<=> j = f(j) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f107,plain,
( m = j
| ~ element(j,m)
| j = f(j)
| k = f(j)
| ~ spl0_11
| ~ spl0_15 ),
inference(resolution,[],[f89,f72]) ).
fof(f124,plain,
spl0_22,
inference(avatar_split_clause,[],[f13,f122]) ).
fof(f13,axiom,
! [X2,X0] :
( ~ element(X2,X0)
| ~ element(X0,X2)
| ~ element(X0,n)
| X0 = X2
| n = X2
| n = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).
fof(f120,plain,
spl0_21,
inference(avatar_split_clause,[],[f8,f118]) ).
fof(f8,axiom,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X0 = X1
| m = X1
| m = X0
| element(X0,m) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_8) ).
fof(f112,plain,
spl0_20,
inference(avatar_split_clause,[],[f16,f110]) ).
fof(f16,axiom,
! [X0] :
( ~ element(X0,k)
| k = X0
| n = X0
| m = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
fof(f106,plain,
spl0_19,
inference(avatar_split_clause,[],[f12,f104]) ).
fof(f12,axiom,
! [X0] :
( n = X0
| element(X0,n)
| element(g(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).
fof(f102,plain,
spl0_18,
inference(avatar_split_clause,[],[f11,f100]) ).
fof(f11,axiom,
! [X0] :
( n = X0
| element(X0,n)
| element(X0,g(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).
fof(f98,plain,
spl0_17,
inference(avatar_split_clause,[],[f10,f96]) ).
fof(f10,axiom,
! [X0] :
( n = X0
| element(X0,n)
| g(X0) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).
fof(f94,plain,
spl0_16,
inference(avatar_split_clause,[],[f9,f92]) ).
fof(f9,axiom,
! [X0] :
( n = X0
| element(X0,n)
| n != g(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_9) ).
fof(f90,plain,
spl0_15,
inference(avatar_split_clause,[],[f7,f88]) ).
fof(f7,axiom,
! [X0] :
( ~ element(X0,m)
| m = X0
| element(f(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_7) ).
fof(f86,plain,
spl0_14,
inference(avatar_split_clause,[],[f6,f84]) ).
fof(f6,axiom,
! [X0] :
( ~ element(X0,m)
| m = X0
| element(X0,f(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_6) ).
fof(f82,plain,
spl0_13,
inference(avatar_split_clause,[],[f5,f80]) ).
fof(f5,axiom,
! [X0] :
( ~ element(X0,m)
| m = X0
| f(X0) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_5) ).
fof(f78,plain,
spl0_12,
inference(avatar_split_clause,[],[f4,f76]) ).
fof(f4,axiom,
! [X0] :
( ~ element(X0,m)
| m = X0
| m != f(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_4) ).
fof(f73,plain,
spl0_11,
inference(avatar_split_clause,[],[f3,f71]) ).
fof(f3,axiom,
! [X0] :
( ~ element(X0,j)
| j = X0
| k = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_3) ).
fof(f69,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f19,f66,f62]) ).
fof(f19,plain,
( n = k
| element(n,k) ),
inference(equality_resolution,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( n != X0
| k = X0
| element(X0,k) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).
fof(f60,plain,
( spl0_8
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f50,f41,f30,f57]) ).
fof(f50,plain,
( element(m,j)
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f43,f32]) ).
fof(f55,plain,
( ~ spl0_7
| ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f49,f45,f30,f52]) ).
fof(f49,plain,
( m != j
| ~ spl0_3
| spl0_6 ),
inference(forward_demodulation,[],[f46,f32]) ).
fof(f46,plain,
( m != k
| spl0_6 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f48,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f45,f41]) ).
fof(f18,plain,
( m = k
| element(m,k) ),
inference(equality_resolution,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( m != X0
| k = X0
| element(X0,k) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).
fof(f39,plain,
( ~ spl0_4
| spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f34,f30,f26,f36]) ).
fof(f34,plain,
( ~ element(j,j)
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f27,f32]) ).
fof(f27,plain,
( ~ element(k,j)
| spl0_2 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f33,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f17,f30,f26]) ).
fof(f17,plain,
( j = k
| element(k,j) ),
inference(equality_resolution,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( k != X0
| j = X0
| element(X0,j) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_2) ).
fof(f24,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f1,f21]) ).
fof(f1,axiom,
m != n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN015-1 : TPTP v8.2.0. Released v1.0.0.
% 0.11/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 14:59:23 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (12667)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (12670)WARNING: value z3 for option sas not known
% 0.13/0.36 % (12668)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36 % (12671)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (12669)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (12670)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)
% 0.13/0.36 % (12672)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)
% 0.13/0.36 % (12673)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)
% 0.13/0.36 % (12674)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)
% 0.13/0.36 TRYING [1]
% 0.13/0.36 TRYING [2]
% 0.13/0.36 TRYING [3]
% 0.13/0.36 TRYING [4]
% 0.13/0.36 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 TRYING [5]
% 0.13/0.37 TRYING [3]
% 0.13/0.37 TRYING [6]
% 0.13/0.37 TRYING [7]
% 0.13/0.37 TRYING [4]
% 0.13/0.37 TRYING [8]
% 0.13/0.38 TRYING [9]
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 TRYING [3]
% 0.13/0.38 TRYING [4]
% 0.13/0.38 TRYING [5]
% 0.13/0.38 TRYING [10]
% 0.13/0.38 TRYING [5]
% 0.13/0.38 TRYING [6]
% 0.13/0.39 TRYING [7]
% 0.13/0.39 TRYING [11]
% 0.13/0.39 TRYING [8]
% 0.13/0.39 % (12672)First to succeed.
% 0.13/0.40 TRYING [6]
% 0.13/0.40 TRYING [9]
% 0.13/0.40 % (12672)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-12667"
% 0.13/0.40 TRYING [12]
% 0.13/0.40 % (12672)Refutation found. Thanks to Tanya!
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.40 % (12672)------------------------------
% 0.13/0.40 % (12672)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.40 % (12672)Termination reason: Refutation
% 0.13/0.40
% 0.13/0.40 % (12672)Memory used [KB]: 1162
% 0.13/0.40 % (12672)Time elapsed: 0.038 s
% 0.13/0.40 % (12672)Instructions burned: 67 (million)
% 0.13/0.40 % (12667)Success in time 0.044 s
%------------------------------------------------------------------------------