%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP228-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 10:13:23 AM UTC 2026
% Result : Unsatisfiable 1.87s 1.30s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 45
% Syntax : Number of formulae : 279 ( 16 unt; 16 def)
% Number of atoms : 967 ( 333 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1323 ( 635 ~; 672 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 75 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( inverse(sk_c1) = sk_c10
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( inverse(sk_c1) = sk_c10
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( inverse(sk_c1) = sk_c10
| sk_c10 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c1) = sk_c10
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f12]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f22,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| inverse(sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c10 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f39,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f40,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| inverse(sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f42,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c10 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c10,sk_c3) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f58,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| inverse(sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f60,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f62,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c10 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f65]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f76,plain,
( sk_c10 = inverse(sk_c2)
| inverse(sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f78,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f80,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f82,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f83]) ).
fof(f93,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(X0) != sk_c10
| multiply(X0,sk_c9) != sk_c10
| multiply(sk_c10,X1) != sk_c9
| multiply(X2,sk_c10) != X1
| inverse(X2) != sk_c10
| inverse(sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X4,X5) != sk_c10
| inverse(X4) != X5
| multiply(X5,sk_c9) != sk_c10
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(sk_c10,X1)
| multiply(X2,sk_c10) != X1
| sk_c10 != inverse(X2)
| inverse(sk_c10) != sk_c9
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c10 != multiply(X5,sk_c9)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(reorient_equations,[],[f93]) ).
fof(f95,plain,
! [X2,X3,X0,X6,X7,X4,X5] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2)
| inverse(sk_c10) != sk_c9
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c10 != multiply(X5,sk_c9)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(equality_resolution,[],[f94]) ).
fof(f96,plain,
! [X2,X3,X0,X6,X7,X4] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2)
| inverse(sk_c10) != sk_c9
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != multiply(X4,inverse(X4))
| sk_c10 != multiply(inverse(X4),sk_c9)
| inverse(X6) != X7
| inverse(X4) != inverse(X7)
| multiply(X6,inverse(X4)) != X7 ),
inference(equality_resolution,[],[f95]) ).
fof(f97,plain,
! [X2,X3,X0,X6,X4] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c9)
| sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2)
| inverse(sk_c10) != sk_c9
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != multiply(X4,inverse(X4))
| sk_c10 != multiply(inverse(X4),sk_c9)
| inverse(X4) != inverse(inverse(X6))
| inverse(X6) != multiply(X6,inverse(X4)) ),
inference(equality_resolution,[],[f96]) ).
fof(f99,definition,
( spl0_1
<=> ! [X6,X4] :
( sk_c10 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c10 != multiply(inverse(X4),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f100,plain,
( ! [X6,X4] :
( sk_c10 != multiply(inverse(X4),sk_c9)
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c10 != multiply(X4,inverse(X4)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_2
<=> ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f103,plain,
( ! [X3] :
( sk_c10 != multiply(X3,sk_c9)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,definition,
( spl0_3
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f106,plain,
( inverse(sk_c10) = sk_c9
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( inverse(sk_c10) != sk_c9
| spl0_3 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f109,definition,
( spl0_4
<=> ! [X2] :
( sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f110,plain,
( ! [X2] :
( sk_c9 != multiply(sk_c10,multiply(X2,sk_c10))
| sk_c10 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f111,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f97,f102,f109,f105,f102,f99]) ).
fof(f117,definition,
( spl0_6
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f119,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f137,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f139,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f84,f117,f137]) ).
fof(f142,definition,
( spl0_11
<=> sk_c10 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f144,plain,
( sk_c10 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f82,f117,f142]) ).
fof(f147,definition,
( spl0_12
<=> sk_c10 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f148,plain,
( sk_c10 != multiply(sk_c4,sk_c9)
| spl0_12 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f149,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f150,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f80,f117,f147]) ).
fof(f152,definition,
( spl0_13
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f154,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f78,f117,f152]) ).
fof(f156,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f76,f117,f105]) ).
fof(f158,definition,
( spl0_14
<=> sk_c3 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f160,plain,
( sk_c3 = multiply(sk_c2,sk_c10)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f165,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f66,f158,f137]) ).
fof(f166,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f64,f158,f142]) ).
fof(f167,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f62,f158,f147]) ).
fof(f168,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f60,f158,f152]) ).
fof(f169,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f58,f158,f105]) ).
fof(f171,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c10,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f173,plain,
( sk_c9 = multiply(sk_c10,sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f178,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f48,f171,f137]) ).
fof(f179,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f46,f171,f142]) ).
fof(f180,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f44,f171,f147]) ).
fof(f181,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f42,f171,f152]) ).
fof(f182,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f40,f171,f105]) ).
fof(f184,definition,
( spl0_16
<=> sk_c10 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f186,plain,
( sk_c10 = multiply(sk_c1,sk_c9)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f191,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f30,f184,f137]) ).
fof(f192,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f28,f184,f142]) ).
fof(f193,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f26,f184,f147]) ).
fof(f194,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f24,f184,f152]) ).
fof(f195,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f22,f184,f105]) ).
fof(f197,definition,
( spl0_17
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f199,plain,
( inverse(sk_c1) = sk_c10
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f204,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f13,f197,f137]) ).
fof(f205,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f11,f197,f142]) ).
fof(f206,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f9,f197,f147]) ).
fof(f207,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f7,f197,f152]) ).
fof(f208,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f5,f197,f105]) ).
fof(f209,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f103,f149]) ).
fof(f212,plain,
( sk_c10 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f209]) ).
fof(f213,plain,
( $false
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f212,f154]) ).
fof(f214,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f213]) ).
fof(f215,plain,
( sk_c10 != sk_c10
| inverse(sk_c1) != sk_c10
| ~ spl0_2
| ~ spl0_16 ),
inference(superposition,[],[f103,f186]) ).
fof(f216,plain,
( inverse(sk_c1) != sk_c10
| ~ spl0_2
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f215]) ).
fof(f217,plain,
( $false
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f216,f199]) ).
fof(f218,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f217]) ).
fof(f219,plain,
( sk_c9 != multiply(sk_c10,sk_c3)
| sk_c10 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f110,f160]) ).
fof(f220,plain,
( sk_c10 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f219,f173]) ).
fof(f221,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f220,f119]) ).
fof(f222,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f221]) ).
fof(f223,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f199]) ).
fof(f224,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f154]) ).
fof(f225,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f139]) ).
fof(f228,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl0_6 ),
inference(superposition,[],[f3,f119]) ).
fof(f231,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f237,plain,
( ! [X0] : multiply(sk_c3,X0) = multiply(sk_c2,multiply(sk_c10,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f160]) ).
fof(f238,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f231,f1]) ).
fof(f245,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f225]) ).
fof(f246,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f245,f1]) ).
fof(f272,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f246,f144]) ).
fof(f307,plain,
( multiply(sk_c2,identity) = multiply(sk_c3,sk_c2)
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[],[f237,f228]) ).
fof(f334,plain,
( sk_c1 = multiply(inverse(sk_c10),identity)
| ~ spl0_17 ),
inference(superposition,[],[f238,f223]) ).
fof(f336,plain,
( sk_c4 = multiply(inverse(sk_c10),identity)
| ~ spl0_13 ),
inference(superposition,[],[f238,f224]) ).
fof(f338,plain,
( sk_c2 = multiply(inverse(sk_c10),identity)
| ~ spl0_6 ),
inference(superposition,[],[f238,f228]) ).
fof(f343,plain,
( sk_c10 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f238,f272]) ).
fof(f351,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f238,f160]) ).
fof(f356,plain,
( sk_c10 = multiply(sk_c10,sk_c3)
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f351,f119]) ).
fof(f362,plain,
( identity = sk_c10
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f343,f3]) ).
fof(f376,plain,
( sk_c10 = sk_c9
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f356,f173]) ).
fof(f379,plain,
( sk_c3 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[],[f238,f356]) ).
fof(f381,plain,
( identity = sk_c3
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f379,f3]) ).
fof(f438,plain,
( sk_c10 = multiply(sk_c1,sk_c10)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f186,f376]) ).
fof(f451,plain,
( ! [X0] : multiply(sk_c3,X0) = X0
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[],[f1,f381]) ).
fof(f452,plain,
( sk_c1 = sk_c4
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f336,f334]) ).
fof(f455,plain,
( sk_c10 != multiply(sk_c1,sk_c9)
| spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(superposition,[],[f148,f452]) ).
fof(f457,plain,
( $false
| spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f455,f186]) ).
fof(f458,plain,
( spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f469,plain,
( sk_c1 = sk_c2
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f338,f334]) ).
fof(f472,plain,
( sk_c3 = multiply(sk_c1,sk_c10)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f160,f469]) ).
fof(f481,plain,
( sk_c10 = sk_c3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f438,f472]) ).
fof(f618,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f451,f481]) ).
fof(f661,plain,
( multiply(sk_c3,sk_c1) = multiply(sk_c1,identity)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f307,f469]) ).
fof(f662,plain,
( multiply(sk_c3,sk_c1) = multiply(sk_c1,sk_c3)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f661,f381]) ).
fof(f663,plain,
( multiply(sk_c10,sk_c1) = multiply(sk_c1,sk_c10)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f662,f481]) ).
fof(f664,plain,
( sk_c3 = multiply(sk_c10,sk_c1)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f663,f472]) ).
fof(f665,plain,
( sk_c1 = sk_c3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f664,f618]) ).
fof(f666,plain,
( sk_c1 = sk_c10
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f665,f481]) ).
fof(f668,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f199,f666]) ).
fof(f717,plain,
( sk_c10 != sk_c9
| spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f107,f668]) ).
fof(f722,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f717,f376]) ).
fof(f723,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f722]) ).
fof(f726,plain,
( ! [X6,X4] :
( sk_c10 != multiply(X4,inverse(X4))
| sk_c10 != multiply(inverse(X4),sk_c10)
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f100,f376]) ).
fof(f728,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c1,sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f726,f199]) ).
fof(f752,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f728,f438]) ).
fof(f756,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f752,f618]) ).
fof(f775,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f756,f119]) ).
fof(f776,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f775,f668]) ).
fof(f780,plain,
( sk_c10 != sk_c3
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f776,f160]) ).
fof(f794,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f780,f481]) ).
fof(f795,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f794]) ).
fof(f807,definition,
( spl0_23
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f808,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f810,definition,
( spl0_24
<=> sk_c10 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f811,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f1009,plain,
( identity != inverse(inverse(sk_c10))
| sk_c10 != inverse(inverse(inverse(sk_c10)))
| ~ spl0_23 ),
inference(superposition,[],[f808,f3]) ).
fof(f1097,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f154]) ).
fof(f1098,plain,
( sk_c10 = multiply(sk_c10,sk_c4)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1097,f362]) ).
fof(f1099,plain,
( sk_c9 = multiply(inverse(sk_c4),sk_c10)
| ~ spl0_12 ),
inference(superposition,[],[f238,f149]) ).
fof(f1101,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1099,f154]) ).
fof(f1102,plain,
( sk_c10 = sk_c9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1101,f811]) ).
fof(f1107,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_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f100,f1102]) ).
fof(f1119,plain,
( ! [X0] :
( identity != sk_c10
| sk_c10 != multiply(sk_c10,inverse(sk_c10))
| inverse(X0) != multiply(X0,inverse(sk_c10))
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(superposition,[],[f1107,f3]) ).
fof(f1122,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,inverse(sk_c10))
| inverse(X0) != multiply(X0,inverse(sk_c10))
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f1119,f362]) ).
fof(f1127,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c9)
| inverse(X0) != multiply(X0,inverse(sk_c10))
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1122,f106]) ).
fof(f1136,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,inverse(sk_c10))
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1127,f1102]) ).
fof(f1140,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,inverse(sk_c10))
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f1136,f811]) ).
fof(f1143,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c9)
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1140,f106]) ).
fof(f1145,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1143,f1102]) ).
fof(f1147,plain,
( ! [X0] :
( sk_c9 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1145,f106]) ).
fof(f1149,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1147,f1102]) ).
fof(f1150,plain,
( spl0_23
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f1149,f810,f152,f147,f142,f137,f105,f99,f807]) ).
fof(f1152,plain,
( identity != inverse(sk_c9)
| sk_c10 != inverse(inverse(inverse(sk_c10)))
| ~ spl0_3
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1009,f106]) ).
fof(f1159,plain,
( identity != inverse(sk_c10)
| sk_c10 != inverse(inverse(inverse(sk_c10)))
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1152,f1102]) ).
fof(f1165,plain,
( identity != sk_c9
| sk_c10 != inverse(inverse(inverse(sk_c10)))
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1159,f106]) ).
fof(f1171,plain,
( identity != sk_c10
| sk_c10 != inverse(inverse(inverse(sk_c10)))
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1165,f1102]) ).
fof(f1176,plain,
( sk_c10 != inverse(inverse(inverse(sk_c10)))
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f1171,f362]) ).
fof(f1181,plain,
( sk_c10 != inverse(inverse(sk_c9))
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1176,f106]) ).
fof(f1187,plain,
( sk_c10 != inverse(inverse(sk_c10))
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1181,f1102]) ).
fof(f1193,plain,
( sk_c10 != inverse(sk_c9)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1187,f106]) ).
fof(f1195,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1193,f1102]) ).
fof(f1197,plain,
( sk_c10 != sk_c9
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1195,f106]) ).
fof(f1200,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f1197,f1102]) ).
fof(f1201,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f1200]) ).
fof(f1221,definition,
( spl0_42
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f1353,plain,
( sk_c4 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f238,f1098]) ).
fof(f1355,plain,
( identity = sk_c4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1353,f3]) ).
fof(f1356,plain,
( sk_c10 = sk_c4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1355,f362]) ).
fof(f1357,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f1098,f1356]) ).
fof(f1363,plain,
( spl0_42
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f1102,f810,f152,f147,f1221]) ).
fof(f1366,plain,
( spl0_24
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f1357,f152,f142,f137,f810]) ).
fof(f1367,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| sk_c10 != inverse(sk_c10)
| ~ spl0_4
| ~ spl0_24 ),
inference(superposition,[],[f110,f811]) ).
fof(f1371,plain,
( sk_c10 != sk_c9
| sk_c10 != inverse(sk_c10)
| ~ spl0_4
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1367,f811]) ).
fof(f1372,plain,
( sk_c10 != sk_c9
| sk_c10 != sk_c9
| ~ spl0_3
| ~ spl0_4
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1371,f106]) ).
fof(f1373,plain,
( sk_c10 != sk_c9
| ~ spl0_3
| ~ spl0_4
| ~ spl0_24 ),
inference(duplicate_literal_removal,[],[f1372]) ).
fof(f1374,plain,
( ~ spl0_42
| ~ spl0_3
| ~ spl0_4
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f1373,f810,f109,f105,f1221]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f111]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f140]) ).
cnf(s8,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f145]) ).
cnf(s9,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f150]) ).
cnf(s10,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f155]) ).
cnf(s11,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f156]) ).
cnf(s16,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f165]) ).
cnf(s17,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f166]) ).
cnf(s18,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f167]) ).
cnf(s19,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f168]) ).
cnf(s20,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f169]) ).
cnf(s25,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f178]) ).
cnf(s26,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f179]) ).
cnf(s27,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f180]) ).
cnf(s28,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f181]) ).
cnf(s29,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f182]) ).
cnf(s34,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f191]) ).
cnf(s35,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f192]) ).
cnf(s36,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f193]) ).
cnf(s37,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f194]) ).
cnf(s38,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f195]) ).
cnf(s43,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f204]) ).
cnf(s44,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f205]) ).
cnf(s45,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f206]) ).
cnf(s46,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f207]) ).
cnf(s47,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f208]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f214]) ).
cnf(s49,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f218]) ).
cnf(s50,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f222]) ).
cnf(s52,plain,
( spl0_12
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f458]) ).
cnf(s54,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f723]) ).
cnf(s59,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f795]) ).
cnf(s109,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f1150]) ).
cnf(s116,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f1201]) ).
cnf(s136,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_24
| spl0_42 ),
inference(sat_conversion,[],[f1363]) ).
cnf(s139,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| spl0_24 ),
inference(sat_conversion,[],[f1366]) ).
cnf(s140,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_24
| ~ spl0_42 ),
inference(sat_conversion,[],[f1374]) ).
cnf(s141,plain,
spl0_3,
inference(rat,[],[s54,s11,s20,s29,s38,s47]) ).
cnf(s143,plain,
( spl0_15
| ~ spl0_4 ),
inference(rat,[],[s136,s140,s139,s25,s26,s27,s28,s141]) ).
cnf(s144,plain,
( spl0_14
| ~ spl0_4 ),
inference(rat,[],[s136,s140,s139,s16,s17,s18,s19,s141]) ).
cnf(s145,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_4 ),
inference(rat,[],[s136,s140,s139,s7,s8,s9,s10,s50,s141]) ).
cnf(s146,plain,
~ spl0_4,
inference(rat,[],[s145,s144,s143]) ).
cnf(s148,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s49,s37,s46]) ).
cnf(s149,plain,
( ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s49,s36,s45,s48]) ).
cnf(s150,plain,
~ spl0_2,
inference(rat,[],[s149,s148]) ).
cnf(s151,plain,
spl0_1,
inference(rat,[],[s2,s141,s146,s150]) ).
cnf(s152,plain,
spl0_13,
inference(rat,[],[s59,s10,s19,s28,s37,s46,s151]) ).
cnf(s153,plain,
( ~ spl0_11
| ~ spl0_24
| ~ spl0_10
| ~ spl0_12 ),
inference(rat,[],[s109,s116,s152,s141,s151]) ).
cnf(s154,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_12 ),
inference(rat,[],[s153,s139,s152]) ).
cnf(s155,plain,
( spl0_11
| ~ spl0_14
| ~ spl0_6
| ~ spl0_15 ),
inference(rat,[],[s59,s35,s44,s151]) ).
cnf(s156,plain,
( ~ spl0_14
| ~ spl0_6
| ~ spl0_15
| ~ spl0_12 ),
inference(rat,[],[s59,s34,s43,s154,s155,s151]) ).
cnf(s157,plain,
( spl0_14
| ~ spl0_12 ),
inference(rat,[],[s154,s16,s17]) ).
cnf(s158,plain,
( spl0_6
| ~ spl0_12 ),
inference(rat,[],[s154,s7,s8]) ).
cnf(s159,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_14 ),
inference(rat,[],[s154,s25,s26,s156]) ).
cnf(s160,plain,
~ spl0_12,
inference(rat,[],[s159,s158,s157]) ).
cnf(s161,plain,
spl0_17,
inference(rat,[],[s45,s160]) ).
cnf(s162,plain,
spl0_16,
inference(rat,[],[s36,s160]) ).
cnf(s166,plain,
$false,
inference(rat,[],[s52,s160,s152,s161,s162]) ).
fof(f1375,plain,
$false,
inference(avatar_sat_refutation,[],[s166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP228-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:37:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.87/1.30 % (4160197)Input is clausal, will run a generic CNF schedule.
% 1.87/1.30 % (4160206)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=756764993:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.87/1.30 % (4160208)dis-21_1_sil=8000:lcm=predicate:random_seed=2295375849: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)
% 1.87/1.30 % (4160208)Refutation not found, incomplete strategy
% 1.87/1.30 % (4160208)------------------------------
% 1.87/1.30 % (4160208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.30 % (4160208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.30 % (4160208)CaDiCaL version: 2.1.3
% 1.87/1.30 % (4160208)Termination reason: Refutation not found, incomplete strategy
% 1.87/1.30 % (4160208)Time elapsed: 0.002 s
% 1.87/1.30 % (4160208)Peak memory usage: 88 MB
% 1.87/1.30 % (4160208)Instructions burned: 3 (million)
% 1.87/1.30 % (4160203)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1666189215:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.87/1.30 % (4160205)lrs+10_1_sil=8000:sp=occurrence:random_seed=2682057940:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.87/1.30 % (4160202)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=3315616046:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.87/1.30 % (4160204)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=531715151:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.87/1.30 % (4160207)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2325077676:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.87/1.30 % (4160206)Instruction limit reached!
% 1.87/1.30 % (4160206)------------------------------
% 1.87/1.30 % (4160206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.30 % (4160206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.30 % (4160206)CaDiCaL version: 2.1.3
% 1.87/1.30 % (4160206)Termination reason: Instruction limit
% 1.87/1.30 % (4160206)Termination phase: Saturation
% 1.87/1.30 % (4160206)Time elapsed: 0.036 s
% 1.87/1.30 % (4160206)Peak memory usage: 89 MB
% 1.87/1.30 % (4160206)Instructions burned: 116 (million)
% 1.87/1.30 % (4160207)First to succeed.
% 1.87/1.30 % (4160207)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4160197"
% 1.87/1.30 % (4160205)Instruction limit reached!
% 1.87/1.30 % (4160205)------------------------------
% 1.87/1.30 % (4160205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.30 % (4160205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.30 % (4160205)CaDiCaL version: 2.1.3
% 1.87/1.30 % (4160205)Termination reason: Instruction limit
% 1.87/1.30 % (4160205)Termination phase: Saturation
% 1.87/1.30 % (4160205)Time elapsed: 0.052 s
% 1.87/1.30 % (4160205)Peak memory usage: 89 MB
% 1.87/1.30 % (4160205)Instructions burned: 107 (million)
% 1.87/1.30 % (4160216)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=1201454498:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 1.87/1.30 % (4160216)Instruction limit reached!
% 1.87/1.30 % (4160216)------------------------------
% 1.87/1.30 % (4160216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.30 % (4160216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.30 % (4160216)CaDiCaL version: 2.1.3
% 1.87/1.30 % (4160216)Termination reason: Instruction limit
% 1.87/1.30 % (4160216)Termination phase: Saturation
% 1.87/1.30 % (4160216)Time elapsed: 0.036 s
% 1.87/1.30 % (4160216)Peak memory usage: 89 MB
% 1.87/1.30 % (4160216)Instructions burned: 144 (million)
% 1.87/1.30 % (4160217)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=952357322:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 1.87/1.30 % (4160217)Refutation not found, incomplete strategy
% 1.87/1.30 % (4160217)------------------------------
% 1.87/1.30 % (4160217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.30 % (4160217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.30 % (4160217)CaDiCaL version: 2.1.3
% 1.87/1.30 % (4160217)Termination reason: Refutation not found, incomplete strategy
% 1.87/1.30 % (4160217)Time elapsed: 0.007 s
% 1.87/1.30 % (4160217)Peak memory usage: 88 MB
% 1.87/1.30 % (4160217)Instructions burned: 9 (million)
% 1.87/1.30 % (4160219)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2131734418:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 1.87/1.30 % (4160208)------------------------------
% 1.87/1.30 % (4160208)------------------------------
% 1.87/1.30 % (4160219)Refutation not found, incomplete strategy
% 1.87/1.30 % (4160219)------------------------------
% 1.87/1.30 % (4160219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.30 % (4160219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.30 % (4160219)CaDiCaL version: 2.1.3
% 1.87/1.30 % (4160219)Termination reason: Refutation not found, incomplete strategy
% 1.87/1.30 % (4160219)Time elapsed: 0.003 s
% 1.87/1.30 % (4160219)Peak memory usage: 88 MB
% 1.87/1.30 % (4160219)Instructions burned: 8 (million)
% 1.87/1.30 % (4160207)Refutation found. Thanks to Tanya!
% 1.87/1.30 % SZS status Unsatisfiable for theBenchmark
% 1.87/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.83/1.50 % (4160207)------------------------------
% 3.83/1.50 % (4160207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.50 % (4160207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.50 % (4160207)CaDiCaL version: 2.1.3
% 3.83/1.50 % (4160207)Termination reason: Refutation
% 3.83/1.50 % (4160207)Time elapsed: 0.029 s
% 3.83/1.50 % (4160207)Peak memory usage: 90 MB
% 3.83/1.50 % (4160207)Instructions burned: 44 (million)
% 3.83/1.50 % (4160207)------------------------------
% 3.83/1.50 % (4160207)------------------------------
% 3.83/1.50 % (4160197)Success in time 0.446 s
% 3.83/1.50 % Vampire exiting
%------------------------------------------------------------------------------