%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP269-1 : 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 : n010.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 10:13:29 AM UTC 2026
% Result : Unsatisfiable 3.91s 1.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 52
% Syntax : Number of formulae : 368 ( 24 unt; 22 def)
% Number of atoms : 1312 ( 372 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1833 ( 889 ~; 922 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 70 !; 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(f9,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/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/sandbox/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(f12,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f14]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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_c11) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f83,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c11 = inverse(sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f88,plain,
( sk_c11 = inverse(sk_c2)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f90,plain,
( sk_c11 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c11 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f93]) ).
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_c11) != sk_c9
| inverse(X1) != sk_c11
| 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/sandbox/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_c9 != multiply(X1,sk_c11)
| sk_c11 != 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_c9 != multiply(X1,sk_c11)
| sk_c11 != 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_c9 != multiply(X1,sk_c11)
| sk_c11 != 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_c9 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f118,plain,
( ! [X1] :
( sk_c9 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1) )
| ~ 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_c11 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f131,plain,
( sk_c11 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f129]) ).
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_c9 = multiply(sk_c2,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f181,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| ~ 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(f210,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f34,f203,f149]) ).
fof(f211,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f32,f203,f154]) ).
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(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(f224,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f15,f217,f149]) ).
fof(f225,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f13,f217,f154]) ).
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(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(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_c11,sk_c2)
| ~ spl0_7 ),
inference(superposition,[],[f3,f131]) ).
fof(f463,plain,
( sk_c11 = multiply(sk_c11,sk_c2)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f462,f357]) ).
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(f473,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f121,f450]) ).
fof(f482,plain,
( sk_c11 = multiply(sk_c2,sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f181,f450]) ).
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(f491,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c11)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f243,f482]) ).
fof(f493,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f491,f131]) ).
fof(f494,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f493,f179,f164,f159,f154,f149,f129,f439]) ).
fof(f497,plain,
( sk_c11 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_23 ),
inference(superposition,[],[f243,f440]) ).
fof(f499,plain,
( identity = sk_c11
| ~ spl0_23 ),
inference(forward_demodulation,[],[f497,f3]) ).
fof(f500,plain,
( sk_c11 != sk_c11
| multiply(sk_c1,sk_c11) != sk_c10
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f115,f205]) ).
fof(f506,plain,
( sk_c11 != sk_c11
| sk_c10 != multiply(sk_c2,sk_c11)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f115,f131]) ).
fof(f507,plain,
( sk_c10 != multiply(sk_c2,sk_c11)
| ~ spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f506]) ).
fof(f508,plain,
( multiply(sk_c1,sk_c11) != sk_c10
| ~ spl0_3
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f500]) ).
fof(f509,plain,
( sk_c11 != sk_c10
| ~ spl0_3
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f507,f482]) ).
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(f533,plain,
( ~ spl0_27
| ~ spl0_3
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f509,f179,f164,f159,f154,f149,f129,f114,f527]) ).
fof(f548,plain,
( spl0_27
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f360,f174,f169,f154,f149,f527]) ).
fof(f608,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_c10,sk_c11)
| sk_c11 != multiply(sk_c4,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_27 ),
inference(superposition,[],[f608,f161]) ).
fof(f625,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(sk_c4,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_27 ),
inference(forward_demodulation,[],[f610,f528]) ).
fof(f641,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c4,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f625,f440]) ).
fof(f648,plain,
( ! [X0] :
( sk_c11 != sk_c9
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f641,f166]) ).
fof(f655,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f648,f450]) ).
fof(f661,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f655,f528]) ).
fof(f666,plain,
( ! [X0] :
( sk_c11 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c11) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_27 ),
inference(forward_demodulation,[],[f661,f528]) ).
fof(f689,plain,
( sk_c11 = sk_c4
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(forward_demodulation,[],[f378,f528]) ).
fof(f715,definition,
( spl0_31
<=> sk_c11 = inverse(sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f716,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f737,definition,
( spl0_33
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f738,plain,
( ! [X0] :
( sk_c11 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c11) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f740,definition,
( spl0_34
<=> sk_c11 = multiply(sk_c2,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f741,plain,
( sk_c11 = multiply(sk_c2,sk_c11)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f740]) ).
fof(f742,plain,
( sk_c11 != multiply(sk_c2,sk_c11)
| spl0_34 ),
inference(avatar_component_clause,[],[f740]) ).
fof(f751,plain,
( sk_c10 = inverse(sk_c11)
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(superposition,[],[f161,f689]) ).
fof(f752,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(forward_demodulation,[],[f751,f528]) ).
fof(f756,plain,
( spl0_31
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f752,f527,f174,f169,f159,f715]) ).
fof(f767,plain,
( identity = multiply(sk_c11,sk_c11)
| ~ spl0_31 ),
inference(superposition,[],[f3,f716]) ).
fof(f769,plain,
( identity = sk_c10
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_31 ),
inference(forward_demodulation,[],[f767,f473]) ).
fof(f773,plain,
( spl0_33
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f666,f527,f439,f164,f159,f154,f149,f108,f737]) ).
fof(f778,plain,
( sk_c11 != inverse(sk_c11)
| sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_31
| ~ spl0_33 ),
inference(superposition,[],[f738,f716]) ).
fof(f780,plain,
( sk_c11 != inverse(sk_c10)
| sk_c10 != multiply(sk_c4,sk_c11)
| ~ spl0_13
| ~ spl0_33 ),
inference(superposition,[],[f738,f161]) ).
fof(f790,plain,
( sk_c11 != inverse(sk_c11)
| sk_c10 != multiply(sk_c4,sk_c11)
| ~ spl0_13
| ~ spl0_27
| ~ spl0_33 ),
inference(forward_demodulation,[],[f780,f528]) ).
fof(f792,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_31
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f778,f716]) ).
fof(f797,plain,
( sk_c10 != multiply(sk_c4,sk_c11)
| ~ spl0_13
| ~ spl0_27
| ~ spl0_31
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f790,f716]) ).
fof(f799,plain,
( $false
| ~ spl0_23
| ~ spl0_31
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f792,f440]) ).
fof(f800,plain,
( ~ spl0_23
| ~ spl0_31
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f799]) ).
fof(f805,plain,
( sk_c10 != multiply(sk_c11,sk_c11)
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27
| ~ spl0_31
| ~ spl0_33 ),
inference(forward_demodulation,[],[f797,f689]) ).
fof(f811,plain,
( $false
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27
| ~ spl0_31
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f805,f473]) ).
fof(f812,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27
| ~ spl0_31
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f811]) ).
fof(f821,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c11)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_27 ),
inference(forward_demodulation,[],[f112,f528]) ).
fof(f858,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,[],[f118,f450]) ).
fof(f860,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_31 ),
inference(superposition,[],[f858,f716]) ).
fof(f861,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,[],[f858,f171]) ).
fof(f869,plain,
( sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f861]) ).
fof(f870,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_31 ),
inference(trivial_inequality_removal,[],[f860]) ).
fof(f876,plain,
( sk_c11 != sk_c10
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f869,f176]) ).
fof(f877,plain,
( $false
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f870,f440]) ).
fof(f878,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f877]) ).
fof(f883,plain,
( $false
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f876,f528]) ).
fof(f884,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f883]) ).
fof(f928,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_18
| ~ spl0_19
| ~ spl0_27 ),
inference(forward_demodulation,[],[f485,f528]) ).
fof(f1017,plain,
( sk_c11 != inverse(sk_c11)
| sk_c11 != multiply(sk_c1,sk_c11)
| ~ spl0_18
| ~ spl0_33 ),
inference(superposition,[],[f738,f205]) ).
fof(f1024,plain,
( sk_c2 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f243,f463]) ).
fof(f1026,plain,
( identity = sk_c2
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1024,f3]) ).
fof(f1027,plain,
( sk_c11 = sk_c2
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1026,f357]) ).
fof(f1034,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f131,f1027]) ).
fof(f1039,plain,
( sk_c11 = sk_c10
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_31 ),
inference(forward_demodulation,[],[f769,f357]) ).
fof(f1040,plain,
( spl0_31
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f1034,f154,f149,f129,f715]) ).
fof(f1043,plain,
( spl0_27
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1039,f715,f164,f159,f154,f149,f120,f527]) ).
fof(f1048,plain,
( sk_c11 = sk_c9
| ~ spl0_17
| ~ spl0_34 ),
inference(forward_demodulation,[],[f181,f741]) ).
fof(f1087,plain,
( ! [X1] :
( sk_c11 != inverse(X1)
| sk_c11 != multiply(X1,sk_c11) )
| ~ spl0_4
| ~ spl0_17
| ~ spl0_34 ),
inference(forward_demodulation,[],[f118,f1048]) ).
fof(f1088,plain,
( sk_c11 = multiply(sk_c11,sk_c2)
| ~ spl0_7
| ~ spl0_23 ),
inference(forward_demodulation,[],[f462,f499]) ).
fof(f1093,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c2,sk_c11)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_17
| ~ spl0_34 ),
inference(superposition,[],[f1087,f131]) ).
fof(f1094,plain,
( sk_c11 != multiply(sk_c2,sk_c11)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_17
| ~ spl0_34 ),
inference(trivial_inequality_removal,[],[f1093]) ).
fof(f1097,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_17
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f1094,f741]) ).
fof(f1098,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_17
| ~ spl0_34 ),
inference(avatar_contradiction_clause,[],[f1097]) ).
fof(f1107,plain,
( ! [X3] :
( sk_c11 != inverse(X3)
| sk_c9 != multiply(X3,sk_c11) )
| ~ spl0_2
| ~ spl0_27 ),
inference(forward_demodulation,[],[f821,f528]) ).
fof(f1110,plain,
( sk_c11 = sk_c9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f367,f499]) ).
fof(f1112,plain,
( spl0_4
| ~ spl0_2
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f1107,f527,f111,f117]) ).
fof(f1115,plain,
( sk_c11 = multiply(sk_c2,sk_c11)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f181,f1110]) ).
fof(f1116,plain,
( spl0_34
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f1115,f439,f179,f164,f159,f740]) ).
fof(f1117,plain,
( spl0_23
| ~ spl0_18
| ~ spl0_19
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f928,f527,f217,f203,f439]) ).
fof(f1121,definition,
( spl0_40
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f1122,plain,
( identity = sk_c11
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f1121]) ).
fof(f1142,plain,
( spl0_40
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f499,f439,f1121]) ).
fof(f1150,plain,
( sk_c11 != sk_c10
| sk_c11 != inverse(sk_c11)
| ~ spl0_18
| ~ spl0_19
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1017,f219]) ).
fof(f1170,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_18
| ~ spl0_19
| ~ spl0_27
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1150,f528]) ).
fof(f1176,definition,
( spl0_41
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f1178,plain,
( sk_c11 != sk_c9
| spl0_41 ),
inference(avatar_component_clause,[],[f1176]) ).
fof(f1188,plain,
( ~ spl0_31
| ~ spl0_18
| ~ spl0_19
| ~ spl0_27
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f1170,f737,f527,f217,f203,f715]) ).
fof(f1196,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f243,f181]) ).
fof(f1198,plain,
( sk_c11 = multiply(sk_c11,sk_c9)
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1196,f131]) ).
fof(f1206,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,[],[f608,f205]) ).
fof(f1214,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,[],[f1206,f219]) ).
fof(f1218,plain,
( ! [X0] :
( 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_subsumption_resolution,[],[f1214,f528]) ).
fof(f1221,plain,
( spl0_33
| ~ spl0_23
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f1218,f527,f217,f203,f108,f439,f737]) ).
fof(f1253,plain,
( sk_c2 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_7
| ~ spl0_23 ),
inference(superposition,[],[f243,f1088]) ).
fof(f1255,plain,
( identity = sk_c2
| ~ spl0_7
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1253,f3]) ).
fof(f1256,plain,
( sk_c11 = sk_c2
| ~ spl0_7
| ~ spl0_23
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1255,f1122]) ).
fof(f1259,plain,
( sk_c9 = multiply(sk_c11,sk_c11)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_40 ),
inference(superposition,[],[f181,f1256]) ).
fof(f1260,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_7
| ~ spl0_23
| ~ spl0_40 ),
inference(superposition,[],[f131,f1256]) ).
fof(f1263,plain,
( sk_c11 = sk_c9
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1259,f440]) ).
fof(f1264,plain,
( spl0_31
| ~ spl0_7
| ~ spl0_23
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f1260,f1121,f439,f129,f715]) ).
fof(f1270,plain,
( sk_c11 != sk_c9
| ~ spl0_17
| spl0_34 ),
inference(forward_demodulation,[],[f742,f181]) ).
fof(f1272,plain,
( ~ spl0_41
| ~ spl0_17
| spl0_34 ),
inference(avatar_split_clause,[],[f1270,f740,f179,f1176]) ).
fof(f1351,plain,
( sk_c11 = sk_c10
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f121,f1198]) ).
fof(f1362,plain,
( $false
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_40
| spl0_41 ),
inference(forward_subsumption_resolution,[],[f1263,f1178]) ).
fof(f1363,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_40
| spl0_41 ),
inference(avatar_contradiction_clause,[],[f1362]) ).
fof(f1365,plain,
( spl0_27
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1351,f179,f129,f120,f527]) ).
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(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(s37,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f210]) ).
cnf(s38,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s39,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f212]) ).
cnf(s40,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f213]) ).
cnf(s47,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f224]) ).
cnf(s48,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f225]) ).
cnf(s49,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f226]) ).
cnf(s50,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f227]) ).
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(s62,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| spl0_23 ),
inference(sat_conversion,[],[f494]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f532]) ).
cnf(s67,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_27 ),
inference(sat_conversion,[],[f533]) ).
cnf(s72,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| spl0_27 ),
inference(sat_conversion,[],[f548]) ).
cnf(s91,plain,
( ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27
| spl0_31 ),
inference(sat_conversion,[],[f756]) ).
cnf(s96,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_27
| spl0_33 ),
inference(sat_conversion,[],[f773]) ).
cnf(s99,plain,
( ~ spl0_23
| ~ spl0_31
| ~ spl0_33 ),
inference(sat_conversion,[],[f800]) ).
cnf(s101,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27
| ~ spl0_31
| ~ spl0_33 ),
inference(sat_conversion,[],[f812]) ).
cnf(s111,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_31 ),
inference(sat_conversion,[],[f878]) ).
cnf(s112,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(sat_conversion,[],[f884]) ).
cnf(s155,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| spl0_31 ),
inference(sat_conversion,[],[f1040]) ).
cnf(s158,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_27
| ~ spl0_31 ),
inference(sat_conversion,[],[f1043]) ).
cnf(s165,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_17
| ~ spl0_34 ),
inference(sat_conversion,[],[f1098]) ).
cnf(s169,plain,
( ~ spl0_2
| spl0_4
| ~ spl0_27 ),
inference(sat_conversion,[],[f1112]) ).
cnf(s172,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_23
| spl0_34 ),
inference(sat_conversion,[],[f1116]) ).
cnf(s173,plain,
( ~ spl0_18
| ~ spl0_19
| spl0_23
| ~ spl0_27 ),
inference(sat_conversion,[],[f1117]) ).
cnf(s182,plain,
( ~ spl0_23
| spl0_40 ),
inference(sat_conversion,[],[f1142]) ).
cnf(s202,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_27
| ~ spl0_31
| ~ spl0_33 ),
inference(sat_conversion,[],[f1188]) ).
cnf(s214,plain,
( ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23
| ~ spl0_27
| spl0_33 ),
inference(sat_conversion,[],[f1221]) ).
cnf(s219,plain,
( ~ spl0_7
| ~ spl0_23
| spl0_31
| ~ spl0_40 ),
inference(sat_conversion,[],[f1264]) ).
cnf(s223,plain,
( ~ spl0_17
| spl0_34
| ~ spl0_41 ),
inference(sat_conversion,[],[f1272]) ).
cnf(s231,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| ~ spl0_40
| spl0_41 ),
inference(sat_conversion,[],[f1363]) ).
cnf(s235,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| spl0_27 ),
inference(sat_conversion,[],[f1365]) ).
cnf(s239,plain,
spl0_5,
inference(rat,[],[s53,s27,s28,s29,s30,s31,s32]) ).
cnf(s240,plain,
( spl0_7
| ~ spl0_4 ),
inference(rat,[],[s112,s72,s7,s8,s9,s10,s11,s12]) ).
cnf(s241,plain,
( ~ spl0_14
| spl0_23
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(rat,[],[s21,s59,s62]) ).
cnf(s242,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_4 ),
inference(rat,[],[s241,s111,s155,s240]) ).
cnf(s243,plain,
( spl0_14
| ~ spl0_4 ),
inference(rat,[],[s231,s182,s173,s223,s235,s165,s20,s40,s50,s240,s239]) ).
cnf(s244,plain,
( spl0_13
| ~ spl0_4 ),
inference(rat,[],[s231,s182,s173,s223,s235,s165,s19,s39,s49,s240,s239]) ).
cnf(s245,plain,
( spl0_12
| ~ spl0_4 ),
inference(rat,[],[s173,s172,s235,s165,s18,s38,s48,s240,s243,s244,s239]) ).
cnf(s246,plain,
~ spl0_4,
inference(rat,[],[s173,s172,s235,s165,s17,s37,s47,s242,s245,s244,s243,s240,s239]) ).
cnf(s247,plain,
( ~ spl0_27
| ~ spl0_14
| ~ spl0_3
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(rat,[],[s57,s21,s22,s67,s239]) ).
cnf(s248,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s247,s158,s155,s239]) ).
cnf(s249,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s66,s40,s50]) ).
cnf(s250,plain,
( spl0_13
| ~ spl0_3 ),
inference(rat,[],[s66,s39,s49]) ).
cnf(s251,plain,
( spl0_12
| ~ spl0_3 ),
inference(rat,[],[s66,s38,s48]) ).
cnf(s252,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s66,s37,s47]) ).
cnf(s253,plain,
( ~ spl0_11
| ~ spl0_3
| ~ spl0_14
| ~ spl0_13
| ~ spl0_12 ),
inference(rat,[],[s57,s11,s12,s248,s239]) ).
cnf(s254,plain,
~ spl0_3,
inference(rat,[],[s253,s252,s251,s250,s249]) ).
cnf(s255,plain,
( spl0_17
| spl0_27 ),
inference(rat,[],[s72,s17,s18,s21,s22]) ).
cnf(s256,plain,
( ~ spl0_17
| spl0_27 ),
inference(rat,[],[s72,s7,s8,s11,s12,s235,s239]) ).
cnf(s257,plain,
spl0_27,
inference(rat,[],[s256,s255]) ).
cnf(s258,plain,
~ spl0_2,
inference(rat,[],[s169,s246,s257]) ).
cnf(s259,plain,
spl0_1,
inference(rat,[],[s2,s246,s239,s254,s258]) ).
cnf(s260,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_7 ),
inference(rat,[],[s96,s99,s241,s155,s259,s257]) ).
cnf(s261,plain,
( spl0_14
| ~ spl0_31 ),
inference(rat,[],[s214,s202,s173,s40,s50,s259,s257]) ).
cnf(s262,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_7 ),
inference(rat,[],[s214,s202,s173,s39,s49,s260,s261,s155,s257,s259]) ).
cnf(s263,plain,
( spl0_12
| ~ spl0_7 ),
inference(rat,[],[s214,s99,s219,s182,s173,s38,s48,s259,s257]) ).
cnf(s264,plain,
( ~ spl0_12
| ~ spl0_7 ),
inference(rat,[],[s214,s99,s219,s182,s173,s37,s47,s262,s257,s259]) ).
cnf(s265,plain,
~ spl0_7,
inference(rat,[],[s264,s263]) ).
cnf(s266,plain,
spl0_16,
inference(rat,[],[s12,s265]) ).
cnf(s267,plain,
spl0_15,
inference(rat,[],[s11,s265]) ).
cnf(s268,plain,
spl0_14,
inference(rat,[],[s10,s265]) ).
cnf(s269,plain,
spl0_13,
inference(rat,[],[s9,s265]) ).
cnf(s270,plain,
spl0_12,
inference(rat,[],[s8,s265]) ).
cnf(s271,plain,
spl0_11,
inference(rat,[],[s7,s265]) ).
cnf(s278,plain,
spl0_31,
inference(rat,[],[s91,s257,s266,s269,s267]) ).
cnf(s279,plain,
~ spl0_33,
inference(rat,[],[s101,s257,s278,s266,s268,s269,s270,s271,s239,s267]) ).
cnf(s280,plain,
spl0_23,
inference(rat,[],[s59,s270,s271,s267]) ).
cnf(s281,plain,
$false,
inference(rat,[],[s96,s268,s257,s280,s270,s271,s259,s269,s279]) ).
fof(f1369,plain,
$false,
inference(avatar_sat_refutation,[],[s281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP269-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 09:44:16 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 3.91/1.40 % (705957)Input is clausal, will run a generic CNF schedule.
% 3.91/1.40 % (705979)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=3145975443:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.91/1.40 % (705985)dis-21_1_sil=8000:lcm=predicate:random_seed=3459445193: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)
% 3.91/1.40 % (705985)Refutation not found, incomplete strategy
% 3.91/1.40 % (705985)------------------------------
% 3.91/1.40 % (705985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.40 % (705985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.40 % (705985)CaDiCaL version: 2.1.3
% 3.91/1.40 % (705985)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.40 % (705985)Time elapsed: 0.003 s
% 3.91/1.40 % (705985)Peak memory usage: 88 MB
% 3.91/1.40 % (705985)Instructions burned: 2 (million)
% 3.91/1.40 % (705983)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1647798062:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.91/1.40 % (705982)lrs+10_1_sil=8000:sp=occurrence:random_seed=2775167021:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.91/1.40 % (705984)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=166529124:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.91/1.40 % (705980)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1881775247:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.91/1.40 % (705982)Refutation not found, incomplete strategy
% 3.91/1.40 % (705982)------------------------------
% 3.91/1.40 % (705982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.40 % (705982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.40 % (705982)CaDiCaL version: 2.1.3
% 3.91/1.40 % (705982)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.40 % (705982)Time elapsed: 0.004 s
% 3.91/1.40 % (705982)Peak memory usage: 88 MB
% 3.91/1.40 % (705982)Instructions burned: 5 (million)
% 3.91/1.40 % (705981)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3383942856:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.91/1.40 % (705984)First to succeed.
% 3.91/1.40 % (705984)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-705957"
% 3.91/1.40 % (705983)Instruction limit reached!
% 3.91/1.40 % (705983)------------------------------
% 3.91/1.40 % (705983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.40 % (705983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.40 % (705983)CaDiCaL version: 2.1.3
% 3.91/1.40 % (705983)Termination reason: Instruction limit
% 3.91/1.40 % (705983)Termination phase: Saturation
% 3.91/1.40 % (705983)Time elapsed: 0.064 s
% 3.91/1.40 % (705983)Peak memory usage: 89 MB
% 3.91/1.40 % (705983)Instructions burned: 114 (million)
% 3.91/1.40 % (705985)------------------------------
% 3.91/1.40 % (705985)------------------------------
% 3.91/1.40 % (705995)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=1313853270:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.91/1.40 % (705995)Refutation not found, incomplete strategy
% 3.91/1.40 % (705995)------------------------------
% 3.91/1.40 % (705995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.40 % (705995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.40 % (705995)CaDiCaL version: 2.1.3
% 3.91/1.40 % (705995)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.40 % (705995)Time elapsed: 0.004 s
% 3.91/1.40 % (705995)Peak memory usage: 88 MB
% 3.91/1.40 % (705995)Instructions burned: 5 (million)
% 3.91/1.40 % (705982)------------------------------
% 3.91/1.40 % (705982)------------------------------
% 3.91/1.40 % (705997)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3644554006:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 3.91/1.40 % (705997)Refutation not found, incomplete strategy
% 3.91/1.40 % (705997)------------------------------
% 3.91/1.40 % (705997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.40 % (705997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.40 % (705997)CaDiCaL version: 2.1.3
% 3.91/1.40 % (705997)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.40 % (705997)Time elapsed: 0.004 s
% 3.91/1.40 % (705997)Peak memory usage: 88 MB
% 3.91/1.40 % (705997)Instructions burned: 6 (million)
% 3.91/1.40 % (705984)Refutation found. Thanks to Tanya!
% 3.91/1.40 % SZS status Unsatisfiable for theBenchmark
% 3.91/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.50 % (705984)------------------------------
% 0.15/1.50 % (705984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (705984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (705984)CaDiCaL version: 2.1.3
% 0.15/1.50 % (705984)Termination reason: Refutation
% 0.15/1.50 % (705984)Time elapsed: 0.051 s
% 0.15/1.50 % (705984)Peak memory usage: 90 MB
% 0.15/1.50 % (705984)Instructions burned: 47 (million)
% 0.15/1.50 % (705984)------------------------------
% 0.15/1.50 % (705984)------------------------------
% 0.15/1.50 % (705957)Success in time 0.543 s
% 0.15/1.50 % Vampire exiting
%------------------------------------------------------------------------------