%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP273-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 10:13:30 AM UTC 2026
% Result : Unsatisfiable 3.40s 1.33s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 55
% Syntax : Number of formulae : 402 ( 23 unt; 24 def)
% Number of atoms : 1524 ( 433 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 2208 (1086 ~;1098 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 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/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f23,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(f24,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c11 = inverse(sk_c1)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f43,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f83,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c9 = inverse(sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c9 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f88,plain,
( sk_c9 = inverse(sk_c2)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f90,plain,
( sk_c9 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c9 = inverse(sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f93]) ).
fof(f95,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
fof(f96,plain,
( sk_c9 = inverse(sk_c2)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f95]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,sk_c9) != sk_c11
| inverse(X1) != sk_c9
| 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(f104,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c11 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| 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,[],[f103]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c11 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| 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,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c11 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| 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,[],[f105]) ).
fof(f108,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(f109,plain,
( ! [X6,X4] :
( sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(X4,inverse(X4)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f112,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f115,plain,
( ! [X2] :
( sk_c11 != inverse(X2)
| sk_c10 != multiply(X2,sk_c11) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,definition,
( spl0_4
<=> ! [X1] :
( sk_c11 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f118,plain,
( ! [X1] :
( sk_c9 != inverse(X1)
| sk_c11 != multiply(X1,sk_c9) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,definition,
( spl0_5
<=> sk_c10 = multiply(sk_c11,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f121,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f122,plain,
( sk_c10 != multiply(sk_c11,sk_c9)
| spl0_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f106,f114,f120,f117,f114,f111,f108]) ).
fof(f129,definition,
( spl0_7
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f131,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f144,definition,
( spl0_10
<=> sk_c11 = multiply(sk_c8,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f146,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f96,f129,f144]) ).
fof(f149,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f151,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f94,f129,f149]) ).
fof(f154,definition,
( spl0_12
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f156,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f157,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f92,f129,f154]) ).
fof(f159,definition,
( spl0_13
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f161,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f90,f129,f159]) ).
fof(f164,definition,
( spl0_14
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f166,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f167,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f88,f129,f164]) ).
fof(f169,definition,
( spl0_15
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f171,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( spl0_15
| spl0_7 ),
inference(avatar_split_clause,[],[f86,f129,f169]) ).
fof(f174,definition,
( spl0_16
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f176,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
( spl0_16
| spl0_7 ),
inference(avatar_split_clause,[],[f84,f129,f174]) ).
fof(f179,definition,
( spl0_17
<=> sk_c11 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f181,plain,
( sk_c11 = multiply(sk_c2,sk_c9)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f186,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f74,f179,f149]) ).
fof(f187,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f72,f179,f154]) ).
fof(f188,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f70,f179,f159]) ).
fof(f189,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f68,f179,f164]) ).
fof(f190,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f66,f179,f169]) ).
fof(f191,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f64,f179,f174]) ).
fof(f196,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f54,f120,f149]) ).
fof(f197,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f52,f120,f154]) ).
fof(f198,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f50,f120,f159]) ).
fof(f199,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f48,f120,f164]) ).
fof(f200,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f46,f120,f169]) ).
fof(f201,plain,
( spl0_16
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f120,f174]) ).
fof(f203,definition,
( spl0_18
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f205,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f212,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f30,f203,f159]) ).
fof(f213,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f28,f203,f164]) ).
fof(f214,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f26,f203,f169]) ).
fof(f215,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f24,f203,f174]) ).
fof(f217,definition,
( spl0_19
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f219,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f226,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f11,f217,f159]) ).
fof(f227,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f9,f217,f164]) ).
fof(f228,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f8,f217,f169]) ).
fof(f229,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f6,f217,f174]) ).
fof(f230,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_15 ),
inference(superposition,[],[f3,f171]) ).
fof(f231,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f161]) ).
fof(f237,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f243,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f237,f1]) ).
fof(f246,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f230]) ).
fof(f247,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f246,f1]) ).
fof(f260,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f247,f176]) ).
fof(f307,plain,
( sk_c3 = multiply(inverse(sk_c11),identity)
| ~ spl0_15 ),
inference(superposition,[],[f243,f230]) ).
fof(f309,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f243,f260]) ).
fof(f310,plain,
( sk_c4 = multiply(inverse(sk_c10),identity)
| ~ spl0_13 ),
inference(superposition,[],[f243,f231]) ).
fof(f314,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_14 ),
inference(superposition,[],[f243,f166]) ).
fof(f317,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_12 ),
inference(superposition,[],[f243,f156]) ).
fof(f334,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f317,f151]) ).
fof(f337,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f314,f161]) ).
fof(f341,plain,
( identity = sk_c10
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f309,f3]) ).
fof(f355,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f243,f334]) ).
fof(f357,plain,
( identity = sk_c11
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f355,f3]) ).
fof(f360,plain,
( sk_c11 = sk_c10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f357,f341]) ).
fof(f365,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f243,f337]) ).
fof(f367,plain,
( identity = sk_c9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f365,f3]) ).
fof(f370,plain,
( sk_c10 = sk_c9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f367,f341]) ).
fof(f373,plain,
( sk_c10 != multiply(sk_c11,sk_c10)
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f122,f370]) ).
fof(f374,plain,
( sk_c11 != sk_c10
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f373,f260]) ).
fof(f376,plain,
( sk_c4 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f310,f341]) ).
fof(f377,plain,
( identity = sk_c4
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f376,f3]) ).
fof(f378,plain,
( sk_c10 = sk_c4
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f377,f341]) ).
fof(f388,plain,
( $false
| spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f360,f374]) ).
fof(f389,plain,
( spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f390,plain,
( sk_c10 = multiply(sk_c11,sk_c10)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f121,f370]) ).
fof(f391,plain,
( sk_c11 = sk_c10
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f390,f260]) ).
fof(f414,plain,
( ! [X2] :
( sk_c11 != inverse(X2)
| sk_c11 != multiply(X2,sk_c11) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f115,f391]) ).
fof(f415,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f414,f171]) ).
fof(f420,plain,
( sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f415]) ).
fof(f426,definition,
( spl0_21
<=> sk_c11 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f427,plain,
( sk_c11 = sk_c8
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f428,plain,
( sk_c11 != sk_c8
| spl0_21 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f433,plain,
( sk_c11 != sk_c10
| ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f420,f176]) ).
fof(f439,definition,
( spl0_23
<=> sk_c11 = multiply(sk_c11,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f440,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f445,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f433,f391]) ).
fof(f446,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f445]) ).
fof(f450,plain,
( sk_c11 = sk_c9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f367,f357]) ).
fof(f451,plain,
( sk_c3 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f307,f357]) ).
fof(f454,plain,
( identity = sk_c3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f451,f3]) ).
fof(f455,plain,
( sk_c11 = sk_c3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f454,f357]) ).
fof(f462,plain,
( identity = multiply(sk_c9,sk_c2)
| ~ spl0_7 ),
inference(superposition,[],[f3,f131]) ).
fof(f465,plain,
( identity = multiply(sk_c11,sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f230,f455]) ).
fof(f467,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f465,f357]) ).
fof(f468,plain,
( spl0_23
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f467,f169,f154,f149,f439]) ).
fof(f483,plain,
( sk_c11 = multiply(inverse(sk_c1),sk_c10)
| ~ spl0_19 ),
inference(superposition,[],[f243,f219]) ).
fof(f485,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f483,f205]) ).
fof(f498,plain,
( sk_c11 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_23 ),
inference(superposition,[],[f243,f440]) ).
fof(f500,plain,
( identity = sk_c11
| ~ spl0_23 ),
inference(forward_demodulation,[],[f498,f3]) ).
fof(f501,plain,
( sk_c11 != sk_c11
| multiply(sk_c1,sk_c11) != sk_c10
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f115,f205]) ).
fof(f508,plain,
( multiply(sk_c1,sk_c11) != sk_c10
| ~ spl0_3
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f501]) ).
fof(f527,definition,
( spl0_27
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f528,plain,
( sk_c11 = sk_c10
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f531,plain,
( $false
| ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f508,f219]) ).
fof(f532,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f531]) ).
fof(f544,plain,
( spl0_27
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f391,f174,f169,f164,f159,f120,f527]) ).
fof(f597,plain,
( sk_c11 = multiply(sk_c8,sk_c11)
| ~ spl0_10
| ~ spl0_27 ),
inference(superposition,[],[f146,f528]) ).
fof(f598,plain,
( sk_c9 = multiply(sk_c4,sk_c11)
| ~ spl0_14
| ~ spl0_27 ),
inference(superposition,[],[f166,f528]) ).
fof(f607,plain,
( sk_c11 = multiply(sk_c4,sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_27 ),
inference(forward_demodulation,[],[f598,f450]) ).
fof(f609,plain,
( ! [X6,X4] :
( sk_c11 != multiply(inverse(X4),sk_c11)
| sk_c11 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_27 ),
inference(forward_demodulation,[],[f109,f528]) ).
fof(f610,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(sk_c3,sk_c11)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_27 ),
inference(superposition,[],[f609,f171]) ).
fof(f612,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c8,sk_c11)
| sk_c11 != multiply(sk_c5,sk_c8)
| inverse(X0) != multiply(X0,sk_c8)
| sk_c8 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_27 ),
inference(superposition,[],[f609,f151]) ).
fof(f625,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c8,sk_c11)
| inverse(X0) != multiply(X0,sk_c8)
| sk_c8 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f612,f156]) ).
fof(f627,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c3,sk_c11)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f610,f440]) ).
fof(f641,plain,
( ! [X0] :
( sk_c11 != sk_c8
| inverse(X0) != multiply(X0,sk_c8)
| sk_c8 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_27 ),
inference(forward_demodulation,[],[f625,f334]) ).
fof(f643,plain,
( ! [X0] :
( sk_c11 != sk_c10
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f627,f176]) ).
fof(f649,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c8)
| sk_c8 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f641,f427]) ).
fof(f651,plain,
( ! [X0] :
( sk_c11 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c11) )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f643,f528]) ).
fof(f657,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c8 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_27 ),
inference(forward_demodulation,[],[f649,f427]) ).
fof(f664,plain,
( ! [X0] :
( sk_c11 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c11) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_21
| ~ spl0_27 ),
inference(forward_demodulation,[],[f657,f427]) ).
fof(f694,plain,
( sk_c11 = sk_c4
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(forward_demodulation,[],[f378,f528]) ).
fof(f695,plain,
( sk_c11 != inverse(sk_c11)
| sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_1
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_27 ),
inference(superposition,[],[f651,f171]) ).
fof(f708,plain,
( sk_c11 != sk_c10
| sk_c11 != inverse(sk_c11)
| ~ spl0_1
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f695,f176]) ).
fof(f715,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_1
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f708,f528]) ).
fof(f722,definition,
( spl0_31
<=> sk_c11 = inverse(sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f723,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f726,definition,
( spl0_32
<=> sk_c11 = multiply(sk_c4,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f730,plain,
( ~ spl0_31
| ~ spl0_1
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f715,f527,f439,f174,f169,f108,f722]) ).
fof(f743,plain,
( ! [X1] :
( sk_c11 != multiply(X1,sk_c11)
| sk_c9 != inverse(X1) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f118,f450]) ).
fof(f744,plain,
( ! [X1] :
( sk_c11 != inverse(X1)
| sk_c11 != multiply(X1,sk_c11) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f743,f450]) ).
fof(f746,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f171,f455]) ).
fof(f747,plain,
( spl0_31
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f746,f169,f154,f149,f722]) ).
fof(f748,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f744,f171]) ).
fof(f755,plain,
( sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f748]) ).
fof(f762,plain,
( sk_c11 != sk_c10
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f755,f176]) ).
fof(f769,plain,
( $false
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f762,f528]) ).
fof(f770,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f769]) ).
fof(f778,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c11) )
| ~ spl0_2
| ~ spl0_27 ),
inference(forward_demodulation,[],[f112,f528]) ).
fof(f779,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c11)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_27 ),
inference(forward_demodulation,[],[f778,f450]) ).
fof(f780,plain,
( ! [X3] :
( sk_c11 != inverse(X3)
| sk_c11 != multiply(X3,sk_c11) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_27 ),
inference(forward_demodulation,[],[f779,f528]) ).
fof(f784,plain,
( sk_c10 = inverse(sk_c11)
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(superposition,[],[f161,f694]) ).
fof(f785,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(forward_demodulation,[],[f784,f528]) ).
fof(f789,plain,
( spl0_31
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f785,f527,f174,f169,f159,f722]) ).
fof(f795,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_27 ),
inference(superposition,[],[f780,f171]) ).
fof(f802,plain,
( sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f795]) ).
fof(f809,plain,
( sk_c11 != sk_c10
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(forward_demodulation,[],[f802,f176]) ).
fof(f816,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f809,f528]) ).
fof(f817,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f816]) ).
fof(f932,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_18 ),
inference(superposition,[],[f3,f205]) ).
fof(f935,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(sk_c1,sk_c11)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_27 ),
inference(superposition,[],[f609,f205]) ).
fof(f1005,plain,
( sk_c11 != inverse(sk_c10)
| sk_c10 != multiply(sk_c4,sk_c11)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21
| ~ spl0_27 ),
inference(superposition,[],[f664,f161]) ).
fof(f1016,plain,
( sk_c11 != inverse(sk_c11)
| sk_c10 != multiply(sk_c4,sk_c11)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1005,f528]) ).
fof(f1024,plain,
( sk_c10 != multiply(sk_c4,sk_c11)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21
| ~ spl0_27
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f1016,f723]) ).
fof(f1033,plain,
( sk_c11 != multiply(sk_c4,sk_c11)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21
| ~ spl0_27
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1024,f528]) ).
fof(f1041,plain,
( ~ spl0_32
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21
| ~ spl0_27
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1033,f722,f527,f426,f159,f154,f149,f108,f726]) ).
fof(f1084,definition,
( spl0_35
<=> ! [X0] :
( sk_c11 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c11) ) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f1085,plain,
( ! [X0] :
( sk_c11 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c11) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1084]) ).
fof(f1142,plain,
( sk_c11 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_27 ),
inference(superposition,[],[f597,f334]) ).
fof(f1152,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_21
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1142,f428]) ).
fof(f1153,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_21
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1152]) ).
fof(f1157,plain,
( spl0_32
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f607,f527,f164,f159,f154,f149,f726]) ).
fof(f1206,plain,
( sk_c11 != inverse(sk_c11)
| sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_31
| ~ spl0_35 ),
inference(superposition,[],[f1085,f723]) ).
fof(f1210,plain,
( sk_c11 != inverse(sk_c9)
| sk_c9 != multiply(sk_c2,sk_c11)
| ~ spl0_7
| ~ spl0_35 ),
inference(superposition,[],[f1085,f131]) ).
fof(f1227,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_31
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f1206,f723]) ).
fof(f1231,plain,
( $false
| ~ spl0_23
| ~ spl0_31
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f1227,f440]) ).
fof(f1232,plain,
( ~ spl0_23
| ~ spl0_31
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f1231]) ).
fof(f1261,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c11,multiply(sk_c9,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f121]) ).
fof(f1262,plain,
( sk_c11 = sk_c9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f367,f500]) ).
fof(f1263,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(superposition,[],[f121,f1262]) ).
fof(f1265,plain,
( sk_c11 = sk_c10
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1263,f440]) ).
fof(f1266,plain,
( spl0_27
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f1265,f439,f164,f159,f120,f527]) ).
fof(f1312,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c11)
| ~ spl0_17 ),
inference(superposition,[],[f243,f181]) ).
fof(f1314,plain,
( sk_c9 = multiply(sk_c9,sk_c11)
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1312,f131]) ).
fof(f1327,definition,
( spl0_43
<=> sk_c11 = multiply(sk_c11,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f1340,definition,
( spl0_46
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_46])],[avatar_definition]) ).
fof(f1341,plain,
( sk_c11 = sk_c9
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f1360,plain,
( sk_c9 = multiply(sk_c9,sk_c2)
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f462,f367]) ).
fof(f1362,plain,
( sk_c2 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f243,f1360]) ).
fof(f1364,plain,
( identity = sk_c2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1362,f3]) ).
fof(f1365,plain,
( sk_c9 = sk_c2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1364,f367]) ).
fof(f1372,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f131,f1365]) ).
fof(f1378,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c9,sk_c10)
| inverse(X0) != multiply(X0,sk_c9)
| sk_c9 != inverse(inverse(X0))
| sk_c11 != multiply(sk_c9,sk_c9) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f109,f1372]) ).
fof(f1408,plain,
( spl0_43
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f485,f217,f203,f1327]) ).
fof(f1426,plain,
( sk_c11 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f243,f1314]) ).
fof(f1428,plain,
( identity = sk_c11
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1426,f3]) ).
fof(f1443,plain,
( sk_c11 = sk_c9
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f367,f1428]) ).
fof(f1450,plain,
( spl0_46
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1443,f179,f164,f159,f129,f1340]) ).
fof(f1493,plain,
( ! [X0] :
( sk_c11 != sk_c10
| sk_c11 != multiply(sk_c11,sk_c11)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_27 ),
inference(forward_demodulation,[],[f935,f219]) ).
fof(f1507,plain,
( sk_c11 != sk_c9
| sk_c9 != multiply(sk_c2,sk_c11)
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1210,f1372]) ).
fof(f1511,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c11,sk_c10)
| inverse(X0) != multiply(X0,sk_c9)
| sk_c9 != inverse(inverse(X0))
| sk_c11 != multiply(sk_c9,sk_c9) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_46 ),
inference(forward_demodulation,[],[f1378,f1341]) ).
fof(f1533,plain,
( spl0_35
| ~ spl0_23
| ~ spl0_27
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f1493,f527,f217,f203,f108,f527,f439,f1084]) ).
fof(f1540,plain,
( sk_c9 != multiply(sk_c2,sk_c11)
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_35
| ~ spl0_46 ),
inference(forward_subsumption_resolution,[],[f1507,f1341]) ).
fof(f1543,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != multiply(sk_c11,sk_c10)
| sk_c9 != inverse(inverse(X0))
| sk_c11 != multiply(sk_c9,sk_c9) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_46 ),
inference(forward_demodulation,[],[f1511,f1341]) ).
fof(f1550,plain,
( sk_c9 != multiply(sk_c9,sk_c11)
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_35
| ~ spl0_46 ),
inference(forward_demodulation,[],[f1540,f1365]) ).
fof(f1552,plain,
( ! [X0] :
( sk_c11 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != multiply(sk_c11,sk_c10)
| sk_c11 != multiply(sk_c9,sk_c9) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_46 ),
inference(forward_demodulation,[],[f1543,f1341]) ).
fof(f1556,plain,
( $false
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_35
| ~ spl0_46 ),
inference(forward_subsumption_resolution,[],[f1550,f1314]) ).
fof(f1557,plain,
( ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_35
| ~ spl0_46 ),
inference(avatar_contradiction_clause,[],[f1556]) ).
fof(f1558,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != multiply(sk_c11,sk_c10) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_46 ),
inference(forward_demodulation,[],[f1552,f1341]) ).
fof(f1562,plain,
( ~ spl0_43
| spl0_35
| ~ spl0_23
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f1558,f1340,f164,f159,f129,f108,f439,f1084,f1327]) ).
fof(f1564,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_46 ),
inference(forward_demodulation,[],[f112,f1341]) ).
fof(f1578,plain,
( sk_c11 != sk_c9
| sk_c10 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_46 ),
inference(superposition,[],[f1564,f166]) ).
fof(f1579,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_46 ),
inference(forward_subsumption_resolution,[],[f1578,f1341]) ).
fof(f1582,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_46 ),
inference(forward_subsumption_resolution,[],[f1579,f161]) ).
fof(f1583,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_46 ),
inference(avatar_contradiction_clause,[],[f1582]) ).
fof(f1588,plain,
( sk_c11 = multiply(sk_c9,sk_c2)
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f462,f1428]) ).
fof(f1589,plain,
( sk_c11 = multiply(sk_c11,sk_c1)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f932,f1428]) ).
fof(f1604,plain,
( sk_c9 != sk_c9
| sk_c11 != multiply(sk_c2,sk_c9)
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f118,f131]) ).
fof(f1605,plain,
( sk_c11 != multiply(sk_c2,sk_c9)
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f1604]) ).
fof(f1606,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1605,f181]) ).
fof(f1607,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1606]) ).
fof(f1662,plain,
( identity = multiply(sk_c11,sk_c11)
| ~ spl0_31 ),
inference(superposition,[],[f3,f723]) ).
fof(f1663,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1662,f1428]) ).
fof(f1666,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_17
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1663,f722,f179,f129,f439]) ).
fof(f1705,plain,
( multiply(sk_c11,sk_c11) = multiply(sk_c10,sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f1261,f1588]) ).
fof(f1708,plain,
( sk_c11 = multiply(sk_c10,sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1705,f440]) ).
fof(f1710,plain,
( sk_c1 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f243,f1589]) ).
fof(f1712,plain,
( identity = sk_c1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1710,f3]) ).
fof(f1714,plain,
( sk_c1 = sk_c11
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1712,f1428]) ).
fof(f1717,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f205,f1714]) ).
fof(f1718,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f219,f1714]) ).
fof(f1719,plain,
( sk_c11 = sk_c10
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1718,f440]) ).
fof(f1724,plain,
( spl0_27
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f1719,f439,f217,f203,f179,f129,f527]) ).
fof(f1758,plain,
( ! [X0] :
( inverse(X0) != sk_c11
| sk_c9 != multiply(X0,sk_c11) )
| ~ spl0_2
| ~ spl0_27 ),
inference(superposition,[],[f112,f528]) ).
fof(f1819,plain,
( sk_c11 = multiply(sk_c11,sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1708,f528]) ).
fof(f1843,plain,
( sk_c11 != sk_c9
| sk_c9 != multiply(sk_c2,sk_c11)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_27 ),
inference(superposition,[],[f1758,f131]) ).
fof(f1860,plain,
( sk_c2 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27 ),
inference(superposition,[],[f243,f1819]) ).
fof(f1862,plain,
( identity = sk_c2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1860,f3]) ).
fof(f1864,plain,
( sk_c11 = sk_c2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1862,f1428]) ).
fof(f1904,plain,
( sk_c9 = inverse(sk_c11)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27 ),
inference(superposition,[],[f131,f1864]) ).
fof(f1905,plain,
( sk_c11 = sk_c9
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1904,f723]) ).
fof(f1925,plain,
( sk_c9 != multiply(sk_c11,sk_c11)
| sk_c11 != sk_c9
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1843,f1864]) ).
fof(f1939,plain,
( spl0_46
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1905,f722,f527,f439,f179,f129,f120,f1340]) ).
fof(f1950,plain,
( sk_c11 != sk_c9
| sk_c11 != sk_c9
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1925,f440]) ).
fof(f1951,plain,
( sk_c11 != sk_c9
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27 ),
inference(duplicate_literal_removal,[],[f1950]) ).
fof(f1962,plain,
( ~ spl0_46
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f1951,f527,f439,f179,f129,f120,f111,f1340]) ).
fof(f1980,plain,
( spl0_31
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f1717,f203,f179,f129,f722]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f123]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f147]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f152]) ).
cnf(s8,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f157]) ).
cnf(s9,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f162]) ).
cnf(s10,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f167]) ).
cnf(s11,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f172]) ).
cnf(s12,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f177]) ).
cnf(s17,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f186]) ).
cnf(s18,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s19,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s20,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f189]) ).
cnf(s21,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s22,plain,
( spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f191]) ).
cnf(s27,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f196]) ).
cnf(s28,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f197]) ).
cnf(s29,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f198]) ).
cnf(s30,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f199]) ).
cnf(s31,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f200]) ).
cnf(s32,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f201]) ).
cnf(s39,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f212]) ).
cnf(s40,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f213]) ).
cnf(s41,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f214]) ).
cnf(s42,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f215]) ).
cnf(s49,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f226]) ).
cnf(s50,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f227]) ).
cnf(s51,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f228]) ).
cnf(s52,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f229]) ).
cnf(s53,plain,
( spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f389]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f446]) ).
cnf(s59,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| spl0_23 ),
inference(sat_conversion,[],[f468]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f532]) ).
cnf(s70,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_27 ),
inference(sat_conversion,[],[f544]) ).
cnf(s84,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_27
| ~ spl0_31 ),
inference(sat_conversion,[],[f730]) ).
cnf(s89,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| spl0_31 ),
inference(sat_conversion,[],[f747]) ).
cnf(s92,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(sat_conversion,[],[f770]) ).
cnf(s96,plain,
( ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27
| spl0_31 ),
inference(sat_conversion,[],[f789]) ).
cnf(s98,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(sat_conversion,[],[f817]) ).
cnf(s110,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_21
| ~ spl0_27
| ~ spl0_31
| ~ spl0_32 ),
inference(sat_conversion,[],[f1041]) ).
cnf(s142,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_21
| ~ spl0_27 ),
inference(sat_conversion,[],[f1153]) ).
cnf(s144,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_27
| spl0_32 ),
inference(sat_conversion,[],[f1157]) ).
cnf(s157,plain,
( ~ spl0_23
| ~ spl0_31
| ~ spl0_35 ),
inference(sat_conversion,[],[f1232]) ).
cnf(s170,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| spl0_27 ),
inference(sat_conversion,[],[f1266]) ).
cnf(s182,plain,
( ~ spl0_18
| ~ spl0_19
| spl0_43 ),
inference(sat_conversion,[],[f1408]) ).
cnf(s186,plain,
( ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| spl0_46 ),
inference(sat_conversion,[],[f1450]) ).
cnf(s218,plain,
( ~ spl0_27
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23
| ~ spl0_1
| ~ spl0_27
| spl0_35 ),
inference(sat_conversion,[],[f1533]) ).
cnf(s219,plain,
( ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23
| ~ spl0_27
| spl0_35 ),
inference(rat,[],[s218]) ).
cnf(s231,plain,
( ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_35
| ~ spl0_46 ),
inference(sat_conversion,[],[f1557]) ).
cnf(s232,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| spl0_35
| ~ spl0_43
| ~ spl0_46 ),
inference(sat_conversion,[],[f1562]) ).
cnf(s244,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_46 ),
inference(sat_conversion,[],[f1583]) ).
cnf(s250,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_17 ),
inference(sat_conversion,[],[f1607]) ).
cnf(s265,plain,
( ~ spl0_7
| ~ spl0_17
| spl0_23
| ~ spl0_31 ),
inference(sat_conversion,[],[f1666]) ).
cnf(s271,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23
| spl0_27 ),
inference(sat_conversion,[],[f1724]) ).
cnf(s296,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27
| ~ spl0_31
| spl0_46 ),
inference(sat_conversion,[],[f1939]) ).
cnf(s300,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_27
| ~ spl0_46 ),
inference(sat_conversion,[],[f1962]) ).
cnf(s310,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| spl0_31 ),
inference(sat_conversion,[],[f1980]) ).
cnf(s323,plain,
spl0_5,
inference(rat,[],[s53,s27,s28,s29,s30,s31,s32]) ).
cnf(s324,plain,
( spl0_7
| ~ spl0_4 ),
inference(rat,[],[s92,s70,s7,s8,s9,s10,s11,s12,s323]) ).
cnf(s325,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s92,s70,s17,s18,s19,s20,s21,s22,s250,s323]) ).
cnf(s326,plain,
~ spl0_4,
inference(rat,[],[s325,s324]) ).
cnf(s328,plain,
( spl0_16
| ~ spl0_3 ),
inference(rat,[],[s66,s42,s52]) ).
cnf(s329,plain,
( spl0_15
| ~ spl0_3 ),
inference(rat,[],[s66,s41,s51]) ).
cnf(s330,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s66,s40,s50]) ).
cnf(s331,plain,
( ~ spl0_14
| ~ spl0_16
| ~ spl0_3
| ~ spl0_15 ),
inference(rat,[],[s66,s39,s49,s57,s323]) ).
cnf(s332,plain,
~ spl0_3,
inference(rat,[],[s331,s330,s329,s328]) ).
cnf(s333,plain,
( spl0_16
| spl0_46
| ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s186,s12,s22]) ).
cnf(s334,plain,
( spl0_17
| ~ spl0_15
| ~ spl0_14
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s98,s17,s18,s70,s333,s244,s323]) ).
cnf(s335,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s98,s7,s8,s186,s334,s70,s333,s244,s323]) ).
cnf(s336,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s186,s11,s21,s335,s244]) ).
cnf(s337,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s296,s300,s271,s265,s310,s10,s20,s40,s50,s323]) ).
cnf(s338,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s296,s300,s271,s265,s310,s9,s19,s39,s49,s336,s323]) ).
cnf(s339,plain,
~ spl0_2,
inference(rat,[],[s338,s337]) ).
cnf(s340,plain,
spl0_1,
inference(rat,[],[s2,s326,s323,s332,s339]) ).
cnf(s341,plain,
( ~ spl0_16
| ~ spl0_7
| ~ spl0_15
| ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s59,s17,s18,s265,s84,s96,s70,s340,s323]) ).
cnf(s342,plain,
( ~ spl0_7
| ~ spl0_15
| ~ spl0_13
| ~ spl0_14 ),
inference(rat,[],[s232,s231,s265,s310,s182,s333,s22,s42,s52,s341,s340]) ).
cnf(s343,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s142,s110,s144,s89,s70,s6,s7,s8,s12,s342,s323,s340]) ).
cnf(s344,plain,
( ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s219,s170,s157,s265,s310,s11,s21,s41,s51,s343,s323,s340]) ).
cnf(s345,plain,
spl0_14,
inference(rat,[],[s271,s219,s157,s265,s310,s10,s20,s40,s50,s340]) ).
cnf(s346,plain,
~ spl0_13,
inference(rat,[],[s344,s345]) ).
cnf(s347,plain,
spl0_19,
inference(rat,[],[s49,s346]) ).
cnf(s348,plain,
spl0_18,
inference(rat,[],[s39,s346]) ).
cnf(s349,plain,
spl0_17,
inference(rat,[],[s19,s346]) ).
cnf(s350,plain,
spl0_7,
inference(rat,[],[s9,s346]) ).
cnf(s352,plain,
spl0_31,
inference(rat,[],[s310,s348,s350,s349]) ).
cnf(s353,plain,
spl0_23,
inference(rat,[],[s265,s352,s350,s349]) ).
cnf(s355,plain,
~ spl0_35,
inference(rat,[],[s157,s352,s353]) ).
cnf(s356,plain,
~ spl0_27,
inference(rat,[],[s219,s355,s348,s340,s347,s353]) ).
cnf(s357,plain,
$false,
inference(rat,[],[s271,s349,s348,s347,s350,s356,s353]) ).
fof(f1996,plain,
$false,
inference(avatar_sat_refutation,[],[s357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP273-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:43:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.40/1.32 % (4162705)Input is clausal, will run a generic CNF schedule.
% 3.40/1.32 % (4162712)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1626886820:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.40/1.32 % (4162710)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1606347390:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.40/1.32 % (4162713)lrs+10_1_sil=8000:sp=occurrence:random_seed=1524311159:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.40/1.32 % (4162714)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2149990568:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.40/1.32 % (4162715)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=919745857:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.40/1.32 % (4162711)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2862193922:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.40/1.32 % (4162716)dis-21_1_sil=8000:lcm=predicate:random_seed=1656801033:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.40/1.32 % (4162716)Refutation not found, incomplete strategy
% 3.40/1.32 % (4162716)------------------------------
% 3.40/1.32 % (4162716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.32 % (4162716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.32 % (4162716)CaDiCaL version: 2.1.3
% 3.40/1.32 % (4162716)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.32 % (4162716)Time elapsed: 0.002 s
% 3.40/1.32 % (4162716)Peak memory usage: 88 MB
% 3.40/1.32 % (4162716)Instructions burned: 2 (million)
% 3.40/1.32 % (4162713)Refutation not found, incomplete strategy
% 3.40/1.32 % (4162713)------------------------------
% 3.40/1.32 % (4162713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.32 % (4162713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.33 % (4162713)CaDiCaL version: 2.1.3
% 3.40/1.33 % (4162713)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.33 % (4162713)Time elapsed: 0.004 s
% 3.40/1.33 % (4162713)Peak memory usage: 88 MB
% 3.40/1.33 % (4162713)Instructions burned: 5 (million)
% 3.40/1.33 % (4162715)First to succeed.
% 3.40/1.33 % (4162715)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4162705"
% 3.40/1.33 % (4162714)Instruction limit reached!
% 3.40/1.33 % (4162714)------------------------------
% 3.40/1.33 % (4162714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.33 % (4162714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.33 % (4162714)CaDiCaL version: 2.1.3
% 3.40/1.33 % (4162714)Termination reason: Instruction limit
% 3.40/1.33 % (4162714)Termination phase: Saturation
% 3.40/1.33 % (4162714)Time elapsed: 0.065 s
% 3.40/1.33 % (4162714)Peak memory usage: 89 MB
% 3.40/1.33 % (4162714)Instructions burned: 115 (million)
% 3.40/1.33 % (4162724)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=896031836:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.40/1.33 % (4162724)Refutation not found, incomplete strategy
% 3.40/1.33 % (4162724)------------------------------
% 3.40/1.33 % (4162724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.33 % (4162724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.33 % (4162724)CaDiCaL version: 2.1.3
% 3.40/1.33 % (4162724)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.33 % (4162724)Time elapsed: 0.004 s
% 3.40/1.33 % (4162724)Peak memory usage: 88 MB
% 3.40/1.33 % (4162724)Instructions burned: 5 (million)
% 3.40/1.33 % (4162713)------------------------------
% 3.40/1.33 % (4162713)------------------------------
% 3.40/1.33 % (4162716)------------------------------
% 3.40/1.33 % (4162716)------------------------------
% 3.40/1.33 % (4162715)Refutation found. Thanks to Tanya!
% 3.40/1.33 % SZS status Unsatisfiable for theBenchmark
% 3.40/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 4.02/1.52 % (4162715)------------------------------
% 4.02/1.52 % (4162715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.52 % (4162715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.52 % (4162715)CaDiCaL version: 2.1.3
% 4.02/1.52 % (4162715)Termination reason: Refutation
% 4.02/1.52 % (4162715)Time elapsed: 0.040 s
% 4.02/1.52 % (4162715)Peak memory usage: 90 MB
% 4.02/1.52 % (4162715)Instructions burned: 64 (million)
% 4.02/1.52 % (4162715)------------------------------
% 4.02/1.52 % (4162715)------------------------------
% 4.02/1.52 % (4162705)Success in time 0.479 s
% 4.02/1.52 % Vampire exiting
%------------------------------------------------------------------------------