%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP340-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 10:17:32 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.53s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 66
% Syntax : Number of formulae : 446 ( 22 unt; 32 def)
% Number of atoms : 1568 ( 431 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 2167 (1045 ~;1090 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 33 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f17]) ).
fof(f24,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f32,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f36]) ).
fof(f44,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f52,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f56]) ).
fof(f64,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f66]) ).
fof(f72,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f74]) ).
fof(f76,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f76]) ).
fof(f78,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f79,plain,
( sk_c10 = inverse(sk_c2)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f78]) ).
fof(f80,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f81,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f80]) ).
fof(f82,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f83,plain,
( sk_c10 = inverse(sk_c2)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f82]) ).
fof(f84,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f86]) ).
fof(f92,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f93,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f92]) ).
fof(f94,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
fof(f95,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f94]) ).
fof(f96,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
fof(f97,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f96]) ).
fof(f104,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(X0) != sk_c11
| multiply(X0,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c11 != multiply(X5,sk_c10)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(reorient_equations,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != X7
| inverse(X4) != inverse(X7)
| multiply(X6,inverse(X4)) != X7 ),
inference(equality_resolution,[],[f105]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X6,X4] :
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X4) != inverse(inverse(X6))
| inverse(X6) != multiply(X6,inverse(X4)) ),
inference(equality_resolution,[],[f106]) ).
fof(f109,definition,
( spl0_1
<=> ! [X6,X4] :
( sk_c11 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f110,plain,
( ! [X6,X4] :
( sk_c11 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f113,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f116,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl0_4
<=> ! [X1] :
( sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f119,plain,
( ! [X1] :
( sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,definition,
( spl0_5
<=> ! [X0] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f122,plain,
( ! [X0] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,definition,
( spl0_6
<=> multiply(sk_c10,sk_c11) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f125,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f126,plain,
( multiply(sk_c10,sk_c11) != sk_c9
| spl0_6 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f107,f124,f121,f118,f115,f112,f109]) ).
fof(f129,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f131,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f133,definition,
( spl0_8
<=> sk_c10 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f135,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f138,definition,
( spl0_9
<=> sk_c8 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f140,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f143,definition,
( spl0_10
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f145,plain,
( inverse(sk_c7) = sk_c6
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f148,definition,
( spl0_11
<=> sk_c11 = multiply(sk_c8,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f150,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f97,f133,f148]) ).
fof(f153,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f155,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f156,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f95,f133,f153]) ).
fof(f158,definition,
( spl0_13
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f159,plain,
( sk_c11 != multiply(sk_c5,sk_c8)
| spl0_13 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f160,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f93,f133,f158]) ).
fof(f163,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f165,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f168,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f170,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f173,definition,
( spl0_16
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f175,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f176,plain,
( spl0_16
| spl0_8 ),
inference(avatar_split_clause,[],[f87,f133,f173]) ).
fof(f178,definition,
( spl0_17
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f179,plain,
( sk_c10 != multiply(sk_c3,sk_c11)
| spl0_17 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f180,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f181,plain,
( spl0_17
| spl0_8 ),
inference(avatar_split_clause,[],[f85,f133,f178]) ).
fof(f183,definition,
( spl0_18
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f185,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f186,plain,
( spl0_7
| spl0_18 ),
inference(avatar_split_clause,[],[f83,f183,f129]) ).
fof(f187,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f81,f183,f138]) ).
fof(f188,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f79,f183,f143]) ).
fof(f189,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f77,f183,f148]) ).
fof(f190,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f75,f183,f153]) ).
fof(f191,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f73,f183,f158]) ).
fof(f194,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f67,f183,f173]) ).
fof(f195,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f65,f183,f178]) ).
fof(f197,definition,
( spl0_19
<=> sk_c11 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f199,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f203,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f57,f197,f148]) ).
fof(f204,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f55,f197,f153]) ).
fof(f205,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f53,f197,f158]) ).
fof(f208,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f47,f197,f173]) ).
fof(f209,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f45,f197,f178]) ).
fof(f211,definition,
( spl0_20
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f213,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f217,plain,
( spl0_11
| spl0_20 ),
inference(avatar_split_clause,[],[f37,f211,f148]) ).
fof(f218,plain,
( spl0_12
| spl0_20 ),
inference(avatar_split_clause,[],[f35,f211,f153]) ).
fof(f219,plain,
( spl0_13
| spl0_20 ),
inference(avatar_split_clause,[],[f33,f211,f158]) ).
fof(f222,plain,
( spl0_16
| spl0_20 ),
inference(avatar_split_clause,[],[f27,f211,f173]) ).
fof(f223,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f25,f211,f178]) ).
fof(f227,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f124,f148]) ).
fof(f228,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f124,f153]) ).
fof(f229,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f124,f158]) ).
fof(f230,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f124,f163]) ).
fof(f231,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f124,f168]) ).
fof(f232,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f124,f173]) ).
fof(f233,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f124,f178]) ).
fof(f234,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_16 ),
inference(superposition,[],[f3,f175]) ).
fof(f236,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_12 ),
inference(superposition,[],[f3,f155]) ).
fof(f237,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f3,f145]) ).
fof(f241,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f242,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f234]) ).
fof(f243,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c11,X0)) = multiply(sk_c10,X0)
| ~ spl0_17 ),
inference(superposition,[],[f4,f180]) ).
fof(f245,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c5,multiply(sk_c8,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f160]) ).
fof(f246,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c8,multiply(sk_c10,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f150]) ).
fof(f248,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f242,f1]) ).
fof(f249,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f241,f1]) ).
fof(f264,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f248,f180]) ).
fof(f269,plain,
( multiply(sk_c3,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f243,f264]) ).
fof(f271,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f269,f180]) ).
fof(f280,plain,
( multiply(sk_c11,sk_c10) = multiply(sk_c5,sk_c11)
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f245,f150]) ).
fof(f285,plain,
( sk_c11 = multiply(sk_c5,sk_c11)
| ~ spl0_11
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f280,f264]) ).
fof(f313,plain,
( sk_c3 = multiply(inverse(sk_c11),identity)
| ~ spl0_16 ),
inference(superposition,[],[f249,f234]) ).
fof(f319,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_15 ),
inference(superposition,[],[f249,f170]) ).
fof(f321,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_13 ),
inference(superposition,[],[f249,f160]) ).
fof(f323,plain,
( sk_c11 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_11
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f249,f285]) ).
fof(f324,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c8),multiply(sk_c11,X0))
| ~ spl0_11 ),
inference(superposition,[],[f249,f246]) ).
fof(f325,plain,
( sk_c10 = multiply(inverse(sk_c8),sk_c11)
| ~ spl0_11 ),
inference(superposition,[],[f249,f150]) ).
fof(f326,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_12 ),
inference(superposition,[],[f249,f236]) ).
fof(f330,plain,
( sk_c7 = multiply(inverse(sk_c6),identity)
| ~ spl0_10 ),
inference(superposition,[],[f249,f237]) ).
fof(f333,plain,
( sk_c7 = multiply(sk_c8,identity)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f330,f140]) ).
fof(f336,plain,
( sk_c11 = multiply(sk_c8,sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f323,f155]) ).
fof(f338,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f321,f155]) ).
fof(f340,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f319,f165]) ).
fof(f371,plain,
( sk_c11 = sk_c8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f336,f338]) ).
fof(f375,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f249,f336]) ).
fof(f377,plain,
( sk_c10 = sk_c11
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f375,f325]) ).
fof(f382,plain,
( sk_c6 = multiply(sk_c7,sk_c11)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f131,f371]) ).
fof(f472,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f126,f377]) ).
fof(f494,plain,
( sk_c10 != sk_c9
| spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f472,f271]) ).
fof(f682,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c8),multiply(sk_c10,X0))
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f324,f377]) ).
fof(f683,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c11),multiply(sk_c10,X0))
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f682,f371]) ).
fof(f684,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c10),multiply(sk_c10,X0))
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f683,f377]) ).
fof(f685,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f684,f249]) ).
fof(f690,plain,
( sk_c10 = sk_c9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f685,f340]) ).
fof(f712,plain,
( $false
| spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f690,f494]) ).
fof(f713,plain,
( spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f712]) ).
fof(f718,plain,
( sk_c11 = sk_c9
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f125,f685]) ).
fof(f720,plain,
( sk_c10 = sk_c9
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f718,f377]) ).
fof(f751,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl0_18 ),
inference(superposition,[],[f3,f185]) ).
fof(f753,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_20 ),
inference(superposition,[],[f3,f213]) ).
fof(f756,plain,
( sk_c11 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_6 ),
inference(superposition,[],[f249,f125]) ).
fof(f757,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c10,multiply(sk_c11,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f125]) ).
fof(f758,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c10)
| ~ spl0_8 ),
inference(superposition,[],[f249,f135]) ).
fof(f760,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f758,f185]) ).
fof(f766,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c11)
| ~ spl0_19 ),
inference(superposition,[],[f249,f199]) ).
fof(f768,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f766,f213]) ).
fof(f769,plain,
( sk_c10 != sk_c11
| sk_c11 != inverse(identity)
| ~ spl0_3 ),
inference(superposition,[],[f116,f1]) ).
fof(f774,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f116,f180]) ).
fof(f776,plain,
( sk_c11 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f774]) ).
fof(f779,plain,
( $false
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f776,f175]) ).
fof(f780,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f779]) ).
fof(f787,definition,
( spl0_22
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f788,plain,
( identity = sk_c10
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f787]) ).
fof(f792,definition,
( spl0_23
<=> sk_c11 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f793,plain,
( sk_c11 = inverse(identity)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f794,plain,
( sk_c11 != inverse(identity)
| spl0_23 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f796,definition,
( spl0_24
<=> sk_c10 = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f797,plain,
( sk_c10 = sk_c11
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f796]) ).
fof(f799,plain,
( ~ spl0_23
| ~ spl0_24
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f769,f115,f796,f792]) ).
fof(f810,definition,
( spl0_27
<=> sk_c11 = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f811,plain,
( sk_c11 = inverse(sk_c10)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f812,plain,
( sk_c11 != inverse(sk_c10)
| spl0_27 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f814,definition,
( spl0_28
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f815,plain,
( sk_c10 = sk_c9
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f814]) ).
fof(f824,plain,
( sk_c1 = multiply(inverse(sk_c11),identity)
| ~ spl0_20 ),
inference(superposition,[],[f249,f753]) ).
fof(f833,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(inverse(sk_c10),multiply(sk_c9,X0))
| ~ spl0_6 ),
inference(superposition,[],[f249,f757]) ).
fof(f904,plain,
( multiply(sk_c10,sk_c10) = multiply(sk_c9,sk_c11)
| ~ spl0_6
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f757,f768]) ).
fof(f910,plain,
( sk_c9 = multiply(sk_c9,sk_c11)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f904,f760]) ).
fof(f936,plain,
( sk_c3 = sk_c1
| ~ spl0_16
| ~ spl0_20 ),
inference(superposition,[],[f824,f313]) ).
fof(f1090,plain,
( multiply(inverse(sk_c8),identity) = multiply(sk_c10,sk_c1)
| ~ spl0_11
| ~ spl0_20 ),
inference(superposition,[],[f324,f753]) ).
fof(f1098,plain,
( sk_c5 = multiply(sk_c10,sk_c1)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1090,f326]) ).
fof(f1346,definition,
( spl0_38
<=> sk_c10 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f1347,plain,
( sk_c10 = sk_c7
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1346]) ).
fof(f1983,plain,
( sk_c10 != multiply(sk_c3,sk_c10)
| spl0_17
| ~ spl0_24 ),
inference(superposition,[],[f179,f797]) ).
fof(f1994,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_20
| ~ spl0_24 ),
inference(superposition,[],[f753,f797]) ).
fof(f1996,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24 ),
inference(superposition,[],[f768,f797]) ).
fof(f2011,plain,
( sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_16
| spl0_17
| ~ spl0_20
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1983,f936]) ).
fof(f2015,plain,
( sk_c10 = multiply(sk_c2,sk_c10)
| ~ spl0_8
| ~ spl0_28 ),
inference(superposition,[],[f135,f815]) ).
fof(f2022,plain,
( sk_c11 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_6
| ~ spl0_28 ),
inference(superposition,[],[f756,f815]) ).
fof(f2026,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(inverse(sk_c10),multiply(sk_c10,X0))
| ~ spl0_6
| ~ spl0_28 ),
inference(superposition,[],[f833,f815]) ).
fof(f2034,plain,
( ! [X0] : multiply(sk_c11,X0) = X0
| ~ spl0_6
| ~ spl0_28 ),
inference(forward_demodulation,[],[f2026,f249]) ).
fof(f2036,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_6
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_demodulation,[],[f2022,f797]) ).
fof(f2039,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl0_6
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_demodulation,[],[f2034,f797]) ).
fof(f2069,plain,
( sk_c10 != sk_c11
| ~ spl0_16
| spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24 ),
inference(superposition,[],[f2011,f199]) ).
fof(f2071,plain,
( $false
| ~ spl0_16
| spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f2069,f797]) ).
fof(f2072,plain,
( ~ spl0_16
| spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f2071]) ).
fof(f2383,plain,
( multiply(sk_c11,sk_c11) = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f833,f910]) ).
fof(f2393,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f2383,f756]) ).
fof(f2395,plain,
( sk_c10 = sk_c11
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f2393,f768]) ).
fof(f2403,plain,
( spl0_24
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f2395,f211,f197,f183,f133,f124,f796]) ).
fof(f2759,plain,
( sk_c10 = sk_c9
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24 ),
inference(superposition,[],[f760,f1996]) ).
fof(f2863,plain,
( spl0_28
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f2759,f796,f211,f197,f183,f133,f814]) ).
fof(f3081,plain,
( identity = sk_c2
| ~ spl0_6
| ~ spl0_18
| ~ spl0_24
| ~ spl0_28 ),
inference(superposition,[],[f2039,f751]) ).
fof(f3272,plain,
( sk_c11 != inverse(sk_c2)
| ~ spl0_6
| ~ spl0_18
| spl0_23
| ~ spl0_24
| ~ spl0_28 ),
inference(superposition,[],[f794,f3081]) ).
fof(f3284,plain,
( sk_c10 != sk_c11
| ~ spl0_6
| ~ spl0_18
| spl0_23
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_demodulation,[],[f3272,f185]) ).
fof(f3293,plain,
( $false
| ~ spl0_6
| ~ spl0_18
| spl0_23
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f3284,f797]) ).
fof(f3294,plain,
( ~ spl0_6
| ~ spl0_18
| spl0_23
| ~ spl0_24
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f3293]) ).
fof(f3302,plain,
( ! [X1] :
( sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c10) )
| ~ spl0_4
| ~ spl0_28 ),
inference(forward_demodulation,[],[f119,f815]) ).
fof(f3310,plain,
( sk_c10 != sk_c8
| sk_c10 != multiply(sk_c5,sk_c10)
| ~ spl0_4
| ~ spl0_12
| ~ spl0_28 ),
inference(superposition,[],[f3302,f155]) ).
fof(f3315,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_4
| ~ spl0_18
| ~ spl0_28 ),
inference(superposition,[],[f3302,f185]) ).
fof(f3316,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_4
| ~ spl0_18
| ~ spl0_28 ),
inference(trivial_inequality_removal,[],[f3315]) ).
fof(f3317,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_18
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f3316,f2015]) ).
fof(f3318,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_18
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f3317]) ).
fof(f3324,plain,
( ! [X6,X4] :
( sk_c10 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) )
| ~ spl0_1
| ~ spl0_24 ),
inference(forward_demodulation,[],[f110,f797]) ).
fof(f3325,plain,
( ! [X6,X4] :
( sk_c10 != multiply(inverse(X4),sk_c10)
| sk_c10 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_24 ),
inference(forward_demodulation,[],[f3324,f797]) ).
fof(f3331,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c2,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f3325,f185]) ).
fof(f3343,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c2,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f3331,f1996]) ).
fof(f3351,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f3343,f2015]) ).
fof(f3413,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(superposition,[],[f3351,f185]) ).
fof(f3414,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f3413,f2015]) ).
fof(f4025,plain,
( sk_c5 = sk_c1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_demodulation,[],[f1098,f2039]) ).
fof(f4029,plain,
( identity = sk_c1
| ~ spl0_6
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_demodulation,[],[f1994,f2039]) ).
fof(f4099,plain,
( sk_c1 = sk_c2
| ~ spl0_6
| ~ spl0_18
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(superposition,[],[f4029,f3081]) ).
fof(f4134,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(superposition,[],[f155,f4025]) ).
fof(f4140,plain,
( sk_c11 = sk_c8
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_demodulation,[],[f4134,f213]) ).
fof(f4141,plain,
( sk_c10 = sk_c8
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_demodulation,[],[f4140,f797]) ).
fof(f4175,plain,
( sk_c11 != multiply(sk_c5,sk_c10)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| spl0_13
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(superposition,[],[f159,f4141]) ).
fof(f4199,plain,
( sk_c11 != multiply(sk_c1,sk_c10)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| spl0_13
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_demodulation,[],[f4175,f4025]) ).
fof(f4207,plain,
( $false
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| spl0_13
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f4199,f199]) ).
fof(f4208,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| spl0_13
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f4207]) ).
fof(f4219,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_6
| ~ spl0_18
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(superposition,[],[f185,f4099]) ).
fof(f4353,plain,
( identity = sk_c10
| ~ spl0_6
| ~ spl0_24
| ~ spl0_28 ),
inference(superposition,[],[f3,f2036]) ).
fof(f4374,plain,
( spl0_22
| ~ spl0_6
| ~ spl0_24
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f4353,f814,f796,f124,f787]) ).
fof(f4377,definition,
( spl0_64
<=> sk_c10 = sk_c1 ),
introduced(definition,[new_symbols(definition,[spl0_64])],[avatar_definition]) ).
fof(f4378,plain,
( sk_c10 = sk_c1
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f4377]) ).
fof(f4389,plain,
( sk_c10 = sk_c1
| ~ spl0_6
| ~ spl0_20
| ~ spl0_22
| ~ spl0_24
| ~ spl0_28 ),
inference(superposition,[],[f4029,f788]) ).
fof(f4390,plain,
( spl0_64
| ~ spl0_6
| ~ spl0_20
| ~ spl0_22
| ~ spl0_24
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f4389,f814,f796,f787,f211,f124,f4377]) ).
fof(f4395,plain,
( sk_c11 = inverse(sk_c10)
| ~ spl0_20
| ~ spl0_64 ),
inference(superposition,[],[f213,f4378]) ).
fof(f4406,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_6
| ~ spl0_18
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28
| ~ spl0_64 ),
inference(superposition,[],[f4219,f4378]) ).
fof(f4407,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28
| ~ spl0_64 ),
inference(forward_subsumption_resolution,[],[f4406,f3414]) ).
fof(f4408,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28
| ~ spl0_64 ),
inference(avatar_contradiction_clause,[],[f4407]) ).
fof(f4415,plain,
( $false
| ~ spl0_20
| spl0_27
| ~ spl0_64 ),
inference(forward_subsumption_resolution,[],[f4395,f812]) ).
fof(f4416,plain,
( ~ spl0_20
| spl0_27
| ~ spl0_64 ),
inference(avatar_contradiction_clause,[],[f4415]) ).
fof(f4426,plain,
( ! [X0] :
( inverse(X0) != sk_c10
| sk_c11 != multiply(X0,sk_c10) )
| ~ spl0_5
| ~ spl0_24 ),
inference(forward_demodulation,[],[f122,f797]) ).
fof(f4427,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_24
| ~ spl0_27 ),
inference(forward_demodulation,[],[f811,f797]) ).
fof(f4432,plain,
( ! [X0] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c10) )
| ~ spl0_5
| ~ spl0_24 ),
inference(forward_demodulation,[],[f4426,f797]) ).
fof(f4435,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_5
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f4432,f185]) ).
fof(f4436,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_5
| ~ spl0_18
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f4435]) ).
fof(f4438,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f4436,f2015]) ).
fof(f4439,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_24
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f4438]) ).
fof(f4445,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c10) )
| ~ spl0_2
| ~ spl0_28 ),
inference(forward_demodulation,[],[f113,f815]) ).
fof(f4448,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_2
| ~ spl0_18
| ~ spl0_28 ),
inference(superposition,[],[f4445,f185]) ).
fof(f4449,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_2
| ~ spl0_18
| ~ spl0_28 ),
inference(trivial_inequality_removal,[],[f4448]) ).
fof(f4451,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_18
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f4449,f2015]) ).
fof(f4452,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_18
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f4451]) ).
fof(f4480,plain,
( multiply(sk_c8,sk_c10) = sk_c7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_22 ),
inference(forward_demodulation,[],[f333,f788]) ).
fof(f4606,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f338,f797]) ).
fof(f4616,plain,
( sk_c6 = multiply(sk_c7,sk_c10)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24 ),
inference(forward_demodulation,[],[f382,f797]) ).
fof(f4636,plain,
( spl0_28
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f720,f178,f173,f158,f153,f148,f124,f814]) ).
fof(f4645,plain,
( sk_c10 = multiply(sk_c5,sk_c10)
| ~ spl0_11
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24 ),
inference(forward_demodulation,[],[f285,f797]) ).
fof(f4727,plain,
( sk_c10 = inverse(sk_c3)
| ~ spl0_16
| ~ spl0_24 ),
inference(forward_demodulation,[],[f175,f797]) ).
fof(f4762,plain,
( sk_c10 = multiply(sk_c3,sk_c10)
| ~ spl0_17
| ~ spl0_24 ),
inference(forward_demodulation,[],[f180,f797]) ).
fof(f4772,plain,
( sk_c11 = inverse(sk_c10)
| ~ spl0_22
| ~ spl0_23 ),
inference(forward_demodulation,[],[f793,f788]) ).
fof(f4795,definition,
( spl0_67
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_67])],[avatar_definition]) ).
fof(f4796,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f4795]) ).
fof(f4812,plain,
( sk_c11 = sk_c7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(forward_demodulation,[],[f4480,f150]) ).
fof(f4853,plain,
( sk_c11 = sk_c8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f4606,f150]) ).
fof(f4919,plain,
( sk_c10 = sk_c7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f4812,f797]) ).
fof(f4929,plain,
( sk_c10 = sk_c8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f4853,f797]) ).
fof(f5017,plain,
( spl0_38
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f4919,f796,f787,f148,f143,f138,f1346]) ).
fof(f5030,definition,
( spl0_70
<=> sk_c10 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_70])],[avatar_definition]) ).
fof(f5132,plain,
( sk_c10 = multiply(inverse(sk_c3),sk_c10)
| ~ spl0_17
| ~ spl0_24 ),
inference(superposition,[],[f249,f4762]) ).
fof(f5134,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24 ),
inference(forward_demodulation,[],[f5132,f4727]) ).
fof(f5135,plain,
( spl0_70
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f5134,f796,f178,f173,f5030]) ).
fof(f5157,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c3,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_24 ),
inference(superposition,[],[f3325,f4727]) ).
fof(f5177,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f5157,f4762]) ).
fof(f5186,plain,
( spl0_67
| ~ spl0_70
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f5177,f796,f178,f173,f109,f5030,f4795]) ).
fof(f5208,definition,
( spl0_71
<=> sk_c10 = multiply(sk_c5,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_71])],[avatar_definition]) ).
fof(f5359,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_24
| ~ spl0_27
| ~ spl0_67 ),
inference(superposition,[],[f4796,f4427]) ).
fof(f5363,plain,
( sk_c10 != inverse(sk_c6)
| sk_c6 != multiply(sk_c7,sk_c10)
| ~ spl0_10
| ~ spl0_67 ),
inference(superposition,[],[f4796,f145]) ).
fof(f5368,plain,
( sk_c10 != sk_c8
| sk_c6 != multiply(sk_c7,sk_c10)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_67 ),
inference(forward_demodulation,[],[f5363,f140]) ).
fof(f5372,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_24
| ~ spl0_27
| ~ spl0_67 ),
inference(forward_subsumption_resolution,[],[f5359,f4427]) ).
fof(f5381,plain,
( ~ spl0_70
| ~ spl0_24
| ~ spl0_27
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f5372,f4795,f810,f796,f5030]) ).
fof(f5433,definition,
( spl0_74
<=> sk_c10 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_74])],[avatar_definition]) ).
fof(f5458,plain,
( sk_c6 = multiply(sk_c10,sk_c10)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24
| ~ spl0_38 ),
inference(forward_demodulation,[],[f4616,f1347]) ).
fof(f5459,plain,
( sk_c6 != multiply(sk_c10,sk_c10)
| sk_c10 != sk_c8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_38
| ~ spl0_67 ),
inference(forward_demodulation,[],[f5368,f1347]) ).
fof(f5466,definition,
( spl0_77
<=> sk_c6 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_77])],[avatar_definition]) ).
fof(f5469,plain,
( ~ spl0_74
| ~ spl0_77
| ~ spl0_9
| ~ spl0_10
| ~ spl0_38
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f5459,f4795,f1346,f143,f138,f5466,f5433]) ).
fof(f5499,plain,
( spl0_24
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f377,f178,f173,f158,f153,f148,f796]) ).
fof(f5543,plain,
( spl0_27
| ~ spl0_22
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f4772,f792,f787,f810]) ).
fof(f5615,plain,
( ~ spl0_71
| ~ spl0_74
| ~ spl0_4
| ~ spl0_12
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f3310,f814,f153,f118,f5433,f5208]) ).
fof(f5640,plain,
( spl0_77
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f5458,f1346,f796,f178,f173,f158,f153,f148,f129,f5466]) ).
fof(f5708,plain,
( spl0_71
| ~ spl0_11
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f4645,f796,f178,f173,f158,f148,f5208]) ).
fof(f5754,plain,
( spl0_74
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f4929,f796,f158,f153,f148,f5433]) ).
fof(f5864,plain,
( sk_c10 != sk_c11
| sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_2
| ~ spl0_16
| ~ spl0_28 ),
inference(superposition,[],[f4445,f175]) ).
fof(f5876,plain,
( sk_c10 != sk_c11
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f5864,f4762]) ).
fof(f5881,plain,
( ~ spl0_24
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f5876,f814,f796,f178,f173,f112,f796]) ).
fof(f5882,plain,
( sk_c10 != sk_c11
| sk_c11 != multiply(sk_c3,sk_c10)
| ~ spl0_5
| ~ spl0_16
| ~ spl0_24 ),
inference(superposition,[],[f122,f4727]) ).
fof(f5903,plain,
( sk_c10 != sk_c11
| sk_c10 != sk_c11
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24 ),
inference(forward_demodulation,[],[f5882,f4762]) ).
fof(f5904,plain,
( sk_c10 != sk_c11
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24 ),
inference(duplicate_literal_removal,[],[f5903]) ).
fof(f5913,plain,
( ~ spl0_24
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f5904,f796,f178,f173,f121,f796]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f127]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f151]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f156]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f161]) ).
cnf(s10,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f176]) ).
cnf(s11,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f181]) ).
cnf(s12,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f186]) ).
cnf(s13,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f187]) ).
cnf(s14,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f188]) ).
cnf(s15,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f189]) ).
cnf(s16,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f190]) ).
cnf(s17,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f191]) ).
cnf(s20,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f194]) ).
cnf(s21,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f195]) ).
cnf(s25,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f203]) ).
cnf(s26,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f204]) ).
cnf(s27,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f205]) ).
cnf(s30,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f208]) ).
cnf(s31,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f209]) ).
cnf(s35,plain,
( spl0_11
| spl0_20 ),
inference(sat_conversion,[],[f217]) ).
cnf(s36,plain,
( spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f218]) ).
cnf(s37,plain,
( spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f219]) ).
cnf(s40,plain,
( spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f222]) ).
cnf(s41,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f223]) ).
cnf(s45,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f227]) ).
cnf(s46,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f228]) ).
cnf(s47,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f229]) ).
cnf(s48,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f230]) ).
cnf(s49,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f231]) ).
cnf(s50,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f232]) ).
cnf(s51,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f233]) ).
cnf(s53,plain,
( spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f713]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f780]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f799]) ).
cnf(s77,plain,
( ~ spl0_16
| spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24 ),
inference(sat_conversion,[],[f2072]) ).
cnf(s86,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| spl0_24 ),
inference(sat_conversion,[],[f2403]) ).
cnf(s93,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24
| spl0_28 ),
inference(sat_conversion,[],[f2863]) ).
cnf(s103,plain,
( ~ spl0_6
| ~ spl0_18
| spl0_23
| ~ spl0_24
| ~ spl0_28 ),
inference(sat_conversion,[],[f3294]) ).
cnf(s104,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_18
| ~ spl0_28 ),
inference(sat_conversion,[],[f3318]) ).
cnf(s139,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| spl0_13
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(sat_conversion,[],[f4208]) ).
cnf(s145,plain,
( ~ spl0_6
| spl0_22
| ~ spl0_24
| ~ spl0_28 ),
inference(sat_conversion,[],[f4374]) ).
cnf(s148,plain,
( ~ spl0_6
| ~ spl0_20
| ~ spl0_22
| ~ spl0_24
| ~ spl0_28
| spl0_64 ),
inference(sat_conversion,[],[f4390]) ).
cnf(s151,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_18
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24
| ~ spl0_28
| ~ spl0_64 ),
inference(sat_conversion,[],[f4408]) ).
cnf(s152,plain,
( ~ spl0_20
| spl0_27
| ~ spl0_64 ),
inference(sat_conversion,[],[f4416]) ).
cnf(s153,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_18
| ~ spl0_24
| ~ spl0_28 ),
inference(sat_conversion,[],[f4439]) ).
cnf(s156,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_18
| ~ spl0_28 ),
inference(sat_conversion,[],[f4452]) ).
cnf(s168,plain,
( ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| spl0_28 ),
inference(sat_conversion,[],[f4636]) ).
cnf(s208,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22
| ~ spl0_24
| spl0_38 ),
inference(sat_conversion,[],[f5017]) ).
cnf(s227,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_24
| spl0_70 ),
inference(sat_conversion,[],[f5135]) ).
cnf(s233,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24
| spl0_67
| ~ spl0_70 ),
inference(sat_conversion,[],[f5186]) ).
cnf(s268,plain,
( ~ spl0_24
| ~ spl0_27
| ~ spl0_67
| ~ spl0_70 ),
inference(sat_conversion,[],[f5381]) ).
cnf(s289,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_38
| ~ spl0_67
| ~ spl0_74
| ~ spl0_77 ),
inference(sat_conversion,[],[f5469]) ).
cnf(s292,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| spl0_24 ),
inference(sat_conversion,[],[f5499]) ).
cnf(s293,plain,
( ~ spl0_22
| ~ spl0_23
| spl0_27 ),
inference(sat_conversion,[],[f5543]) ).
cnf(s311,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_28
| ~ spl0_71
| ~ spl0_74 ),
inference(sat_conversion,[],[f5615]) ).
cnf(s315,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24
| ~ spl0_38
| spl0_77 ),
inference(sat_conversion,[],[f5640]) ).
cnf(s330,plain,
( ~ spl0_11
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24
| spl0_71 ),
inference(sat_conversion,[],[f5708]) ).
cnf(s343,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24
| spl0_74 ),
inference(sat_conversion,[],[f5754]) ).
cnf(s377,plain,
( ~ spl0_24
| ~ spl0_16
| ~ spl0_17
| ~ spl0_2
| ~ spl0_24
| ~ spl0_28 ),
inference(sat_conversion,[],[f5881]) ).
cnf(s378,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24
| ~ spl0_28 ),
inference(rat,[],[s377]) ).
cnf(s385,plain,
( ~ spl0_24
| ~ spl0_16
| ~ spl0_17
| ~ spl0_5
| ~ spl0_24 ),
inference(sat_conversion,[],[f5913]) ).
cnf(s386,plain,
( ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_24 ),
inference(rat,[],[s385]) ).
cnf(s387,plain,
spl0_6,
inference(rat,[],[s53,s45,s46,s47,s48,s49,s50,s51]) ).
cnf(s388,plain,
( spl0_8
| ~ spl0_5 ),
inference(rat,[],[s292,s386,s5,s6,s7,s10,s11]) ).
cnf(s389,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_5 ),
inference(rat,[],[s292,s386]) ).
cnf(s390,plain,
( ~ spl0_16
| ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_5 ),
inference(rat,[],[s86,s77,s21,s31,s41,s389,s388,s387]) ).
cnf(s391,plain,
( spl0_16
| ~ spl0_5 ),
inference(rat,[],[s153,s93,s86,s20,s30,s40,s388,s387]) ).
cnf(s392,plain,
( spl0_13
| ~ spl0_5 ),
inference(rat,[],[s77,s386,s86,s17,s27,s37,s388,s391,s387]) ).
cnf(s393,plain,
( spl0_12
| ~ spl0_5 ),
inference(rat,[],[s77,s386,s86,s16,s26,s36,s388,s391,s387]) ).
cnf(s394,plain,
~ spl0_5,
inference(rat,[],[s77,s386,s86,s15,s25,s35,s390,s393,s392,s391,s388,s387]) ).
cnf(s395,plain,
( spl0_24
| ~ spl0_16
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(rat,[],[s86,s11,s21,s31,s41,s292,s387]) ).
cnf(s396,plain,
( ~ spl0_17
| ~ spl0_16
| ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_4 ),
inference(rat,[],[s311,s330,s168,s343,s395,s387]) ).
cnf(s397,plain,
( ~ spl0_16
| ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_4 ),
inference(rat,[],[s77,s31,s41,s396,s395]) ).
cnf(s398,plain,
( spl0_16
| ~ spl0_4 ),
inference(rat,[],[s93,s104,s86,s10,s20,s30,s40,s387]) ).
cnf(s399,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s93,s104,s86,s7,s17,s27,s37,s387]) ).
cnf(s400,plain,
( spl0_12
| ~ spl0_4 ),
inference(rat,[],[s93,s104,s86,s6,s16,s26,s36,s387]) ).
cnf(s401,plain,
( ~ spl0_12
| ~ spl0_4
| ~ spl0_16
| ~ spl0_13 ),
inference(rat,[],[s93,s104,s86,s5,s15,s25,s35,s397,s387]) ).
cnf(s402,plain,
~ spl0_4,
inference(rat,[],[s401,s400,s399,s398]) ).
cnf(s404,plain,
( spl0_16
| ~ spl0_3 ),
inference(rat,[],[s57,s103,s93,s86,s10,s20,s30,s40,s387]) ).
cnf(s405,plain,
( ~ spl0_16
| ~ spl0_3 ),
inference(rat,[],[s86,s77,s11,s21,s31,s41,s55,s387]) ).
cnf(s406,plain,
~ spl0_3,
inference(rat,[],[s405,s404]) ).
cnf(s409,plain,
( spl0_17
| ~ spl0_24
| ~ spl0_16 ),
inference(rat,[],[s77,s31,s41]) ).
cnf(s410,plain,
( spl0_13
| spl0_28
| ~ spl0_24 ),
inference(rat,[],[s93,s7,s17,s27,s37]) ).
cnf(s411,plain,
( spl0_12
| spl0_28
| ~ spl0_24 ),
inference(rat,[],[s93,s6,s16,s26,s36]) ).
cnf(s412,plain,
( ~ spl0_17
| ~ spl0_24
| ~ spl0_2
| ~ spl0_16 ),
inference(rat,[],[s93,s5,s15,s25,s35,s168,s411,s410,s378,s387]) ).
cnf(s413,plain,
( ~ spl0_24
| ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s412,s409]) ).
cnf(s414,plain,
( spl0_13
| spl0_24 ),
inference(rat,[],[s86,s7,s17,s27,s37,s387]) ).
cnf(s415,plain,
( spl0_12
| spl0_24 ),
inference(rat,[],[s86,s6,s16,s26,s36,s387]) ).
cnf(s416,plain,
( ~ spl0_12
| spl0_24
| ~ spl0_13
| ~ spl0_16 ),
inference(rat,[],[s86,s5,s15,s25,s35,s395,s387]) ).
cnf(s417,plain,
( ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s416,s415,s414,s413]) ).
cnf(s418,plain,
~ spl0_2,
inference(rat,[],[s93,s156,s86,s10,s20,s30,s40,s417,s387]) ).
cnf(s419,plain,
spl0_1,
inference(rat,[],[s1,s387,s402,s394,s406,s418]) ).
cnf(s420,plain,
( ~ spl0_11
| ~ spl0_13
| ~ spl0_12
| ~ spl0_24
| ~ spl0_16 ),
inference(rat,[],[s315,s289,s208,s12,s13,s14,s103,s293,s145,s168,s343,s268,s233,s227,s409,s387,s419]) ).
cnf(s421,plain,
( spl0_64
| ~ spl0_28
| ~ spl0_20
| ~ spl0_24 ),
inference(rat,[],[s145,s148,s387]) ).
cnf(s422,plain,
( spl0_11
| spl0_27
| ~ spl0_24 ),
inference(rat,[],[s421,s93,s152,s5,s15,s25,s35]) ).
cnf(s423,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_24 ),
inference(rat,[],[s139,s410,s27,s37,s420,s387]) ).
cnf(s424,plain,
( ~ spl0_70
| ~ spl0_17
| ~ spl0_16
| ~ spl0_24 ),
inference(rat,[],[s421,s152,s411,s36,s423,s422,s268,s233,s419]) ).
cnf(s425,plain,
( ~ spl0_17
| ~ spl0_24
| ~ spl0_16 ),
inference(rat,[],[s424,s227]) ).
cnf(s426,plain,
( ~ spl0_24
| ~ spl0_16 ),
inference(rat,[],[s425,s409]) ).
cnf(s427,plain,
~ spl0_16,
inference(rat,[],[s416,s415,s414,s426]) ).
cnf(s428,plain,
spl0_20,
inference(rat,[],[s40,s427]) ).
cnf(s429,plain,
spl0_19,
inference(rat,[],[s30,s427]) ).
cnf(s430,plain,
spl0_18,
inference(rat,[],[s20,s427]) ).
cnf(s431,plain,
spl0_8,
inference(rat,[],[s10,s427]) ).
cnf(s432,plain,
spl0_24,
inference(rat,[],[s86,s429,s428,s431,s387,s430]) ).
cnf(s433,plain,
spl0_28,
inference(rat,[],[s93,s432,s429,s428,s430,s431]) ).
cnf(s435,plain,
~ spl0_64,
inference(rat,[],[s151,s432,s430,s429,s428,s433,s387,s419,s431]) ).
cnf(s441,plain,
$false,
inference(rat,[],[s421,s432,s428,s433,s435]) ).
fof(f5914,plain,
$false,
inference(avatar_sat_refutation,[],[s441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP340-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:49:50 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.53 % (2296186)Will run a generic schedule for satisfiability detection.
% 0.18/0.53 % (2296196)% WARNING: option uhcvi not known.
% 0.18/0.53 % (2296196)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2670191038:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.53 % (2296195)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1157224515_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.53 % (2296197)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1798359048:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.53 % (2296201)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=556964027:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.53 % (2296200)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3165631819:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.53 % (2296199)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1510354870:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.53 % TRYING [1]
% 0.18/0.53 % TRYING [2]
% 0.18/0.53 % TRYING [3]
% 0.18/0.53 % (2296198)dis+10_1_sil=32000:sp=arity:random_seed=4266103211:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.53 % TRYING [4]
% 0.18/0.53 % TRYING [5]
% 0.18/0.53 % (2296196) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2296186-2296196"...
% 0.18/0.53 % (2296196)...printing done.
% 0.18/0.53 % (2296196)Refutation found. Thanks to Tanya!
% 0.18/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.53 % (2296196)------------------------------
% 0.18/0.53 % (2296196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.53 % (2296196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.53 % (2296196)CaDiCaL version: 2.1.3
% 0.18/0.53 % (2296196)Termination reason: Refutation
% 0.18/0.53 % (2296196)Time elapsed: 0.064 s
% 0.18/0.53 % (2296196)Peak memory usage: 14 MB
% 0.18/0.53 % (2296196)Instructions burned: 210 (million)
% 0.18/0.53 % (2296186)Success in time 0.095 s
% 0.18/0.53 % Vampire exiting
%------------------------------------------------------------------------------