%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP350-1 : 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:43 AM UTC 2026
% Result : Unsatisfiable 3.05s 1.25s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 71
% Syntax : Number of formulae : 483 ( 22 unt; 28 def)
% Number of atoms : 1698 ( 489 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 2329 (1114 ~;1187 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 29 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/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,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f24,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = inverse(sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c9 = inverse(sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c9 = inverse(sk_c10)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c9 = inverse(sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c9 = inverse(sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c9 = inverse(sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c9 = inverse(sk_c10)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f36]) ).
fof(f44,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f54]) ).
fof(f64,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c11 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f74]) ).
fof(f84,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f86]) ).
fof(f88,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f89,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f88]) ).
fof(f90,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f91,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f90]) ).
fof(f92,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f93,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f92]) ).
fof(f94,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f95,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f94]) ).
fof(f104,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f104]) ).
fof(f106,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
fof(f107,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f106]) ).
fof(f108,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_53) ).
fof(f109,plain,
( sk_c10 = inverse(sk_c2)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f108]) ).
fof(f110,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
fof(f111,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f110]) ).
fof(f124,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
fof(f125,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f124]) ).
fof(f126,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_62) ).
fof(f127,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f126]) ).
fof(f128,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_63) ).
fof(f129,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f128]) ).
fof(f130,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_64) ).
fof(f131,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f130]) ).
fof(f144,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(sk_c10,sk_c11) != sk_c9
| inverse(sk_c10) != sk_c9
| multiply(sk_c9,sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(X0,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_71) ).
fof(f145,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(sk_c10,sk_c11) != sk_c9
| sk_c9 != inverse(sk_c10)
| sk_c10 != multiply(sk_c9,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c11 != multiply(X5,sk_c10)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(reorient_equations,[],[f144]) ).
fof(f146,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( multiply(sk_c10,sk_c11) != sk_c9
| sk_c9 != inverse(sk_c10)
| sk_c10 != multiply(sk_c9,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != X7
| inverse(X4) != inverse(X7)
| multiply(X6,inverse(X4)) != X7 ),
inference(equality_resolution,[],[f145]) ).
fof(f147,plain,
! [X2,X3,X0,X1,X6,X4] :
( multiply(sk_c10,sk_c11) != sk_c9
| sk_c9 != inverse(sk_c10)
| sk_c10 != multiply(sk_c9,sk_c11)
| inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X4) != inverse(inverse(X6))
| inverse(X6) != multiply(X6,inverse(X4)) ),
inference(equality_resolution,[],[f146]) ).
fof(f149,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(f150,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,[],[f149]) ).
fof(f152,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f153,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f156,plain,
( ! [X2] :
( sk_c11 != inverse(X2)
| sk_c10 != multiply(X2,sk_c11) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,definition,
( spl0_4
<=> ! [X1] :
( sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f159,plain,
( ! [X1] :
( sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c9) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,definition,
( spl0_5
<=> ! [X0] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f162,plain,
( ! [X0] :
( inverse(X0) != sk_c11
| sk_c11 != multiply(X0,sk_c10) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,definition,
( spl0_6
<=> sk_c10 = multiply(sk_c9,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f165,plain,
( sk_c10 = multiply(sk_c9,sk_c11)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f166,plain,
( sk_c10 != multiply(sk_c9,sk_c11)
| spl0_6 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f168,definition,
( spl0_7
<=> sk_c9 = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f169,plain,
( sk_c9 = inverse(sk_c10)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f170,plain,
( sk_c9 != inverse(sk_c10)
| spl0_7 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f172,definition,
( spl0_8
<=> multiply(sk_c10,sk_c11) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f173,plain,
( multiply(sk_c10,sk_c11) = sk_c9
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f174,plain,
( multiply(sk_c10,sk_c11) != sk_c9
| spl0_8 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f147,f172,f168,f164,f161,f158,f155,f152,f149]) ).
fof(f181,definition,
( spl0_10
<=> sk_c10 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f183,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f196,definition,
( spl0_13
<=> sk_c11 = multiply(sk_c8,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f198,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f201,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f203,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f206,definition,
( spl0_15
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f208,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f211,definition,
( spl0_16
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f213,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f214,plain,
( spl0_16
| spl0_10 ),
inference(avatar_split_clause,[],[f131,f181,f211]) ).
fof(f216,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f218,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f219,plain,
( spl0_17
| spl0_10 ),
inference(avatar_split_clause,[],[f129,f181,f216]) ).
fof(f221,definition,
( spl0_18
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f223,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f224,plain,
( spl0_18
| spl0_10 ),
inference(avatar_split_clause,[],[f127,f181,f221]) ).
fof(f226,definition,
( spl0_19
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f228,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f229,plain,
( spl0_19
| spl0_10 ),
inference(avatar_split_clause,[],[f125,f181,f226]) ).
fof(f231,definition,
( spl0_20
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f233,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f240,plain,
( spl0_16
| spl0_20 ),
inference(avatar_split_clause,[],[f111,f231,f211]) ).
fof(f241,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f109,f231,f216]) ).
fof(f242,plain,
( spl0_18
| spl0_20 ),
inference(avatar_split_clause,[],[f107,f231,f221]) ).
fof(f243,plain,
( spl0_19
| spl0_20 ),
inference(avatar_split_clause,[],[f105,f231,f226]) ).
fof(f245,definition,
( spl0_21
<=> sk_c11 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f247,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f252,plain,
( spl0_14
| spl0_21 ),
inference(avatar_split_clause,[],[f95,f245,f201]) ).
fof(f253,plain,
( spl0_15
| spl0_21 ),
inference(avatar_split_clause,[],[f93,f245,f206]) ).
fof(f254,plain,
( spl0_16
| spl0_21 ),
inference(avatar_split_clause,[],[f91,f245,f211]) ).
fof(f255,plain,
( spl0_17
| spl0_21 ),
inference(avatar_split_clause,[],[f89,f245,f216]) ).
fof(f256,plain,
( spl0_18
| spl0_21 ),
inference(avatar_split_clause,[],[f87,f245,f221]) ).
fof(f257,plain,
( spl0_19
| spl0_21 ),
inference(avatar_split_clause,[],[f85,f245,f226]) ).
fof(f259,definition,
( spl0_22
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f261,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f266,plain,
( spl0_14
| spl0_22 ),
inference(avatar_split_clause,[],[f75,f259,f201]) ).
fof(f267,plain,
( spl0_15
| spl0_22 ),
inference(avatar_split_clause,[],[f73,f259,f206]) ).
fof(f268,plain,
( spl0_16
| spl0_22 ),
inference(avatar_split_clause,[],[f71,f259,f211]) ).
fof(f269,plain,
( spl0_17
| spl0_22 ),
inference(avatar_split_clause,[],[f69,f259,f216]) ).
fof(f270,plain,
( spl0_18
| spl0_22 ),
inference(avatar_split_clause,[],[f67,f259,f221]) ).
fof(f271,plain,
( spl0_19
| spl0_22 ),
inference(avatar_split_clause,[],[f65,f259,f226]) ).
fof(f276,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f55,f164,f201]) ).
fof(f277,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f53,f164,f206]) ).
fof(f278,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f51,f164,f211]) ).
fof(f279,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f49,f164,f216]) ).
fof(f280,plain,
( spl0_18
| spl0_6 ),
inference(avatar_split_clause,[],[f47,f164,f221]) ).
fof(f281,plain,
( spl0_19
| spl0_6 ),
inference(avatar_split_clause,[],[f45,f164,f226]) ).
fof(f285,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f37,f168,f196]) ).
fof(f286,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f35,f168,f201]) ).
fof(f287,plain,
( spl0_15
| spl0_7 ),
inference(avatar_split_clause,[],[f33,f168,f206]) ).
fof(f288,plain,
( spl0_16
| spl0_7 ),
inference(avatar_split_clause,[],[f31,f168,f211]) ).
fof(f289,plain,
( spl0_17
| spl0_7 ),
inference(avatar_split_clause,[],[f29,f168,f216]) ).
fof(f290,plain,
( spl0_18
| spl0_7 ),
inference(avatar_split_clause,[],[f27,f168,f221]) ).
fof(f291,plain,
( spl0_19
| spl0_7 ),
inference(avatar_split_clause,[],[f25,f168,f226]) ).
fof(f296,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f16,f172,f201]) ).
fof(f297,plain,
( spl0_15
| spl0_8 ),
inference(avatar_split_clause,[],[f14,f172,f206]) ).
fof(f298,plain,
( spl0_16
| spl0_8 ),
inference(avatar_split_clause,[],[f12,f172,f211]) ).
fof(f299,plain,
( spl0_17
| spl0_8 ),
inference(avatar_split_clause,[],[f10,f172,f216]) ).
fof(f300,plain,
( spl0_18
| spl0_8 ),
inference(avatar_split_clause,[],[f8,f172,f221]) ).
fof(f301,plain,
( spl0_19
| spl0_8 ),
inference(avatar_split_clause,[],[f6,f172,f226]) ).
fof(f302,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_18 ),
inference(superposition,[],[f3,f223]) ).
fof(f304,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_14 ),
inference(superposition,[],[f3,f203]) ).
fof(f309,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f310,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c11,X0)) = multiply(sk_c10,X0)
| ~ spl0_19 ),
inference(superposition,[],[f4,f228]) ).
fof(f311,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c10,X0)) = multiply(sk_c9,X0)
| ~ spl0_17 ),
inference(superposition,[],[f4,f218]) ).
fof(f315,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f309,f1]) ).
fof(f318,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_18 ),
inference(superposition,[],[f4,f302]) ).
fof(f319,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_18 ),
inference(forward_demodulation,[],[f318,f1]) ).
fof(f332,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f319,f228]) ).
fof(f341,plain,
( multiply(sk_c3,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f310,f332]) ).
fof(f343,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f341,f228]) ).
fof(f358,plain,
( multiply(sk_c4,sk_c10) = multiply(sk_c9,sk_c10)
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f311,f343]) ).
fof(f360,plain,
( sk_c9 = multiply(sk_c9,sk_c10)
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f358,f218]) ).
fof(f381,plain,
( sk_c3 = multiply(inverse(sk_c11),identity)
| ~ spl0_18 ),
inference(superposition,[],[f315,f302]) ).
fof(f383,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f315,f332]) ).
fof(f387,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f315,f218]) ).
fof(f389,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_15 ),
inference(superposition,[],[f315,f208]) ).
fof(f394,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_14 ),
inference(superposition,[],[f315,f304]) ).
fof(f406,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f389,f203]) ).
fof(f408,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f387,f213]) ).
fof(f412,plain,
( identity = sk_c10
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f383,f3]) ).
fof(f427,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f315,f406]) ).
fof(f429,plain,
( identity = sk_c11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f427,f3]) ).
fof(f432,plain,
( sk_c10 = sk_c11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f429,f412]) ).
fof(f433,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f174,f432]) ).
fof(f440,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f406,f432]) ).
fof(f441,plain,
( sk_c11 = sk_c8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f440,f198]) ).
fof(f443,plain,
( sk_c10 != sk_c9
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f433,f343]) ).
fof(f444,plain,
( sk_c10 = sk_c8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f441,f432]) ).
fof(f447,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f315,f408]) ).
fof(f449,plain,
( identity = sk_c9
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f447,f3]) ).
fof(f452,plain,
( sk_c10 = sk_c9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f449,f412]) ).
fof(f466,plain,
( sk_c3 = multiply(inverse(sk_c11),sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f381,f412]) ).
fof(f467,plain,
( sk_c3 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f466,f432]) ).
fof(f468,plain,
( identity = sk_c3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f467,f3]) ).
fof(f469,plain,
( sk_c10 = sk_c3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f468,f412]) ).
fof(f482,plain,
( $false
| spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f443,f452]) ).
fof(f483,plain,
( spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f482]) ).
fof(f484,plain,
( sk_c10 != multiply(sk_c9,sk_c10)
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f166,f432]) ).
fof(f485,plain,
( sk_c10 = multiply(sk_c10,sk_c11)
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f173,f452]) ).
fof(f486,plain,
( sk_c10 != sk_c9
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f484,f360]) ).
fof(f488,plain,
( $false
| spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f486,f452]) ).
fof(f489,plain,
( spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f488]) ).
fof(f491,plain,
( sk_c10 != inverse(sk_c10)
| spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f170,f452]) ).
fof(f514,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c10)
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f394,f412]) ).
fof(f515,plain,
( sk_c5 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f514,f444]) ).
fof(f516,plain,
( identity = sk_c5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f515,f3]) ).
fof(f517,plain,
( sk_c10 = sk_c5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f516,f412]) ).
fof(f522,plain,
( sk_c8 = inverse(sk_c10)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f203,f517]) ).
fof(f523,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f522,f444]) ).
fof(f528,plain,
( $false
| spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f523,f491]) ).
fof(f529,plain,
( spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f528]) ).
fof(f533,plain,
( ! [X0] :
( inverse(X0) != sk_c10
| sk_c11 != multiply(X0,sk_c10) )
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f162,f432]) ).
fof(f534,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f169,f452]) ).
fof(f535,plain,
( ! [X0] :
( inverse(X0) != sk_c10
| sk_c10 != multiply(X0,sk_c10) )
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f533,f432]) ).
fof(f551,plain,
( sk_c10 != sk_c11
| sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f535,f223]) ).
fof(f562,plain,
( sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f551,f432]) ).
fof(f570,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f562,f469]) ).
fof(f576,plain,
( $false
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f570,f343]) ).
fof(f577,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f576]) ).
fof(f665,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c10) )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f153,f452]) ).
fof(f668,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f665,f213]) ).
fof(f672,plain,
( sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f668]) ).
fof(f677,plain,
( sk_c10 != sk_c9
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f672,f218]) ).
fof(f684,plain,
( $false
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f677,f452]) ).
fof(f685,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f684]) ).
fof(f696,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f156,f432]) ).
fof(f697,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c10) )
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f696,f432]) ).
fof(f699,plain,
( sk_c10 != sk_c11
| sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f697,f223]) ).
fof(f710,plain,
( sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f699,f432]) ).
fof(f718,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f710,f469]) ).
fof(f724,plain,
( $false
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f718,f343]) ).
fof(f725,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f724]) ).
fof(f728,plain,
( ! [X1] :
( sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c10) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f159,f452]) ).
fof(f731,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f728,f213]) ).
fof(f735,plain,
( sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f731]) ).
fof(f740,plain,
( sk_c10 != sk_c9
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f735,f218]) ).
fof(f747,plain,
( $false
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f740,f452]) ).
fof(f748,plain,
( ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f747]) ).
fof(f764,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl0_20 ),
inference(superposition,[],[f3,f233]) ).
fof(f769,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c11)
| ~ spl0_21 ),
inference(superposition,[],[f315,f247]) ).
fof(f770,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c1,multiply(sk_c10,X0))
| ~ spl0_21 ),
inference(superposition,[],[f4,f247]) ).
fof(f771,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f769,f261]) ).
fof(f777,plain,
( sk_c11 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f315,f485]) ).
fof(f779,plain,
( identity = sk_c11
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f777,f3]) ).
fof(f782,plain,
( sk_c10 = sk_c11
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f779,f412]) ).
fof(f827,plain,
( ! [X6,X4] :
( sk_c10 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f150,f782]) ).
fof(f828,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_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f827,f782]) ).
fof(f829,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f828,f534]) ).
fof(f838,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(duplicate_literal_removal,[],[f829]) ).
fof(f847,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f838,f343]) ).
fof(f899,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f847,f213]) ).
fof(f908,plain,
( sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f899,f534]) ).
fof(f917,plain,
( sk_c10 != sk_c9
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f908,f218]) ).
fof(f926,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f917,f452]) ).
fof(f927,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f926]) ).
fof(f943,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl0_7 ),
inference(superposition,[],[f3,f169]) ).
fof(f944,plain,
( sk_c9 = multiply(sk_c9,sk_c10)
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f943,f449]) ).
fof(f946,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c9,multiply(sk_c11,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f165]) ).
fof(f949,plain,
( sk_c11 = multiply(inverse(sk_c10),sk_c9)
| ~ spl0_8 ),
inference(superposition,[],[f315,f173]) ).
fof(f950,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c10,multiply(sk_c11,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f173]) ).
fof(f951,plain,
( sk_c11 = multiply(sk_c9,sk_c9)
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f949,f169]) ).
fof(f953,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c10)
| ~ spl0_10 ),
inference(superposition,[],[f315,f183]) ).
fof(f955,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f953,f233]) ).
fof(f961,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c11,sk_c10)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0))
| sk_c11 != multiply(sk_c1,sk_c11) )
| ~ spl0_1
| ~ spl0_22 ),
inference(superposition,[],[f150,f261]) ).
fof(f973,definition,
( spl0_25
<=> sk_c11 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f974,plain,
( sk_c11 = multiply(sk_c10,sk_c10)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f978,definition,
( spl0_26
<=> sk_c11 = multiply(sk_c1,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f980,plain,
( sk_c11 != multiply(sk_c1,sk_c11)
| spl0_26 ),
inference(avatar_component_clause,[],[f978]) ).
fof(f982,definition,
( spl0_27
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f983,plain,
( ! [X0] :
( sk_c11 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c11) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f982]) ).
fof(f985,definition,
( spl0_28
<=> sk_c11 = multiply(sk_c11,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f986,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f985]) ).
fof(f988,plain,
( ~ spl0_26
| spl0_27
| ~ spl0_28
| ~ spl0_1
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f961,f259,f149,f985,f982,f978]) ).
fof(f1014,definition,
( spl0_34
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f1015,plain,
( sk_c11 = sk_c9
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f1026,definition,
( spl0_37
<=> sk_c10 = sk_c11 ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f1027,plain,
( sk_c10 = sk_c11
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1026]) ).
fof(f1035,plain,
( sk_c10 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f315,f944]) ).
fof(f1037,plain,
( identity = sk_c10
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1035,f3]) ).
fof(f1043,plain,
( sk_c10 = sk_c9
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f1037,f449]) ).
fof(f1054,plain,
( multiply(sk_c1,sk_c10) = multiply(sk_c11,sk_c9)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(superposition,[],[f770,f408]) ).
fof(f1063,plain,
( multiply(sk_c1,sk_c10) = multiply(sk_c11,sk_c10)
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1054,f1043]) ).
fof(f1068,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1063,f247]) ).
fof(f1073,plain,
( spl0_28
| ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f1068,f245,f216,f211,f168,f985]) ).
fof(f1075,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_28 ),
inference(superposition,[],[f315,f986]) ).
fof(f1077,plain,
( identity = sk_c10
| ~ spl0_28 ),
inference(forward_demodulation,[],[f1075,f3]) ).
fof(f1149,plain,
( sk_c10 = multiply(sk_c9,sk_c10)
| ~ spl0_6
| ~ spl0_37 ),
inference(superposition,[],[f165,f1027]) ).
fof(f1150,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_8
| ~ spl0_37 ),
inference(superposition,[],[f173,f1027]) ).
fof(f1160,plain,
( sk_c11 = sk_c9
| ~ spl0_8
| ~ spl0_25
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1150,f974]) ).
fof(f1221,plain,
( sk_c10 = sk_c9
| ~ spl0_8
| ~ spl0_25
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1160,f1027]) ).
fof(f1228,definition,
( spl0_42
<=> sk_c10 = multiply(sk_c9,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f1229,plain,
( sk_c10 = multiply(sk_c9,sk_c10)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1228]) ).
fof(f1230,plain,
( sk_c10 != multiply(sk_c9,sk_c10)
| spl0_42 ),
inference(avatar_component_clause,[],[f1228]) ).
fof(f1239,definition,
( spl0_44
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
fof(f1240,plain,
( identity = sk_c10
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1239]) ).
fof(f1246,plain,
( spl0_44
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f1077,f985,f1239]) ).
fof(f1290,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_8
| ~ spl0_25
| ~ spl0_37
| spl0_42 ),
inference(forward_demodulation,[],[f1230,f1221]) ).
fof(f1294,plain,
( sk_c10 != sk_c11
| ~ spl0_8
| ~ spl0_25
| ~ spl0_37
| spl0_42 ),
inference(forward_demodulation,[],[f1290,f974]) ).
fof(f1299,plain,
( $false
| ~ spl0_8
| ~ spl0_25
| ~ spl0_37
| spl0_42 ),
inference(forward_subsumption_resolution,[],[f1294,f1027]) ).
fof(f1300,plain,
( ~ spl0_8
| ~ spl0_25
| ~ spl0_37
| spl0_42 ),
inference(avatar_contradiction_clause,[],[f1299]) ).
fof(f1329,plain,
( sk_c11 != inverse(sk_c9)
| multiply(sk_c10,sk_c11) != sk_c9
| ~ spl0_7
| ~ spl0_27 ),
inference(superposition,[],[f983,f169]) ).
fof(f1345,plain,
( sk_c11 != inverse(sk_c9)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1329,f173]) ).
fof(f1347,definition,
( spl0_50
<=> sk_c10 = multiply(sk_c2,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f1348,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1347]) ).
fof(f1349,plain,
( sk_c10 != multiply(sk_c2,sk_c11)
| spl0_50 ),
inference(avatar_component_clause,[],[f1347]) ).
fof(f1384,plain,
( sk_c2 = multiply(inverse(sk_c10),identity)
| ~ spl0_20 ),
inference(superposition,[],[f315,f764]) ).
fof(f1387,plain,
( sk_c2 = multiply(sk_c9,identity)
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1384,f169]) ).
fof(f1403,plain,
( multiply(sk_c10,sk_c11) = multiply(sk_c9,sk_c10)
| ~ spl0_6
| ~ spl0_21
| ~ spl0_22 ),
inference(superposition,[],[f946,f771]) ).
fof(f1408,plain,
( identity = multiply(sk_c10,sk_c11)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1403,f943]) ).
fof(f1410,plain,
( identity = sk_c9
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1408,f173]) ).
fof(f1415,plain,
( multiply(sk_c9,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22 ),
inference(superposition,[],[f950,f771]) ).
fof(f1426,plain,
( sk_c11 = multiply(sk_c9,sk_c11)
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1415,f974]) ).
fof(f1428,plain,
( sk_c10 = sk_c11
| ~ spl0_6
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1426,f165]) ).
fof(f1432,plain,
( sk_c10 = sk_c9
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_44 ),
inference(superposition,[],[f1240,f1410]) ).
fof(f1443,plain,
( spl0_42
| ~ spl0_6
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f1149,f1026,f164,f1228]) ).
fof(f1462,plain,
( sk_c10 != multiply(sk_c1,sk_c10)
| spl0_26
| ~ spl0_37 ),
inference(superposition,[],[f980,f1027]) ).
fof(f1466,plain,
( sk_c10 != sk_c11
| ~ spl0_21
| spl0_26
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1462,f247]) ).
fof(f1468,plain,
( $false
| ~ spl0_21
| spl0_26
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1466,f1027]) ).
fof(f1469,plain,
( ~ spl0_21
| spl0_26
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1468]) ).
fof(f1482,plain,
( identity = sk_c10
| ~ spl0_7
| ~ spl0_42 ),
inference(superposition,[],[f943,f1229]) ).
fof(f1492,plain,
( sk_c11 != inverse(sk_c10)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_27
| ~ spl0_44 ),
inference(superposition,[],[f1345,f1432]) ).
fof(f1493,plain,
( sk_c11 != sk_c9
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_27
| ~ spl0_44 ),
inference(forward_demodulation,[],[f1492,f169]) ).
fof(f1500,plain,
( spl0_44
| ~ spl0_7
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f1482,f1228,f168,f1239]) ).
fof(f1571,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c9,multiply(sk_c10,X0))
| ~ spl0_42 ),
inference(superposition,[],[f4,f1229]) ).
fof(f1580,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_8
| ~ spl0_42 ),
inference(superposition,[],[f1571,f173]) ).
fof(f1587,plain,
( sk_c11 = sk_c9
| ~ spl0_7
| ~ spl0_8
| ~ spl0_42 ),
inference(forward_demodulation,[],[f1580,f951]) ).
fof(f1599,plain,
( ~ spl0_34
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_27
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f1493,f1239,f982,f259,f245,f172,f168,f164,f1014]) ).
fof(f1600,plain,
( spl0_34
| ~ spl0_7
| ~ spl0_8
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f1587,f1228,f172,f168,f1014]) ).
fof(f1605,plain,
( spl0_37
| ~ spl0_6
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1428,f973,f259,f245,f172,f164,f1026]) ).
fof(f1622,plain,
( identity = multiply(sk_c11,sk_c10)
| ~ spl0_7
| ~ spl0_34 ),
inference(superposition,[],[f943,f1015]) ).
fof(f1624,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_34 ),
inference(superposition,[],[f951,f1015]) ).
fof(f1629,plain,
( sk_c10 = sk_c11
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1624,f771]) ).
fof(f1630,plain,
( sk_c9 = multiply(sk_c11,sk_c10)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1622,f1410]) ).
fof(f1632,plain,
( spl0_37
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1629,f1014,f259,f245,f172,f168,f1026]) ).
fof(f1633,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1630,f1015]) ).
fof(f1634,plain,
( spl0_28
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1633,f1014,f259,f245,f172,f168,f164,f985]) ).
fof(f1638,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c1,sk_c10)
| ~ spl0_5
| ~ spl0_22 ),
inference(superposition,[],[f162,f261]) ).
fof(f1640,plain,
( sk_c11 != multiply(sk_c1,sk_c10)
| ~ spl0_5
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f1638]) ).
fof(f1641,plain,
( $false
| ~ spl0_5
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1640,f247]) ).
fof(f1642,plain,
( ~ spl0_5
| ~ spl0_21
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1641]) ).
fof(f1656,plain,
( ! [X1] :
( sk_c10 != multiply(X1,sk_c11)
| sk_c10 != inverse(X1) )
| ~ spl0_4
| ~ spl0_34 ),
inference(forward_demodulation,[],[f159,f1015]) ).
fof(f1672,plain,
( ! [X1] :
( sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c10) )
| ~ spl0_4
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1656,f1027]) ).
fof(f1688,plain,
( sk_c10 != sk_c9
| sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_34
| ~ spl0_37 ),
inference(superposition,[],[f1672,f169]) ).
fof(f1701,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_25
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1688,f1221]) ).
fof(f1704,plain,
( sk_c10 != sk_c9
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_25
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1701,f955]) ).
fof(f1708,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_25
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1704,f1221]) ).
fof(f1709,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_25
| ~ spl0_34
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1708]) ).
fof(f1710,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_34 ),
inference(forward_demodulation,[],[f153,f1015]) ).
fof(f1711,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c10) )
| ~ spl0_2
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1710,f1027]) ).
fof(f1715,plain,
( sk_c10 != sk_c11
| sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_2
| ~ spl0_22
| ~ spl0_34
| ~ spl0_37 ),
inference(superposition,[],[f1711,f261]) ).
fof(f1718,plain,
( sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_2
| ~ spl0_22
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1715,f1027]) ).
fof(f1722,plain,
( sk_c10 != sk_c11
| ~ spl0_2
| ~ spl0_21
| ~ spl0_22
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1718,f247]) ).
fof(f1725,plain,
( $false
| ~ spl0_2
| ~ spl0_21
| ~ spl0_22
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1722,f1027]) ).
fof(f1726,plain,
( ~ spl0_2
| ~ spl0_21
| ~ spl0_22
| ~ spl0_34
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1725]) ).
fof(f1730,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_37 ),
inference(forward_demodulation,[],[f156,f1027]) ).
fof(f1731,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c10) )
| ~ spl0_3
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1730,f1027]) ).
fof(f1735,plain,
( sk_c10 != sk_c11
| sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_3
| ~ spl0_22
| ~ spl0_37 ),
inference(superposition,[],[f1731,f261]) ).
fof(f1738,plain,
( sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_3
| ~ spl0_22
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1735,f1027]) ).
fof(f1742,plain,
( sk_c10 != sk_c11
| ~ spl0_3
| ~ spl0_21
| ~ spl0_22
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1738,f247]) ).
fof(f1745,plain,
( $false
| ~ spl0_3
| ~ spl0_21
| ~ spl0_22
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f1742,f1027]) ).
fof(f1746,plain,
( ~ spl0_3
| ~ spl0_21
| ~ spl0_22
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1745]) ).
fof(f1756,plain,
( identity != sk_c10
| ~ spl0_7
| spl0_42 ),
inference(forward_demodulation,[],[f1230,f943]) ).
fof(f1763,plain,
( $false
| ~ spl0_7
| spl0_42
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f1756,f1240]) ).
fof(f1764,plain,
( ~ spl0_7
| spl0_42
| ~ spl0_44 ),
inference(avatar_contradiction_clause,[],[f1763]) ).
fof(f1790,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c10)
| ~ spl0_50 ),
inference(superposition,[],[f315,f1348]) ).
fof(f1792,plain,
( sk_c11 = multiply(sk_c10,sk_c10)
| ~ spl0_20
| ~ spl0_50 ),
inference(forward_demodulation,[],[f1790,f233]) ).
fof(f1793,plain,
( spl0_25
| ~ spl0_20
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1792,f1347,f231,f973]) ).
fof(f1802,plain,
( sk_c2 = multiply(sk_c9,sk_c9)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1387,f1410]) ).
fof(f1803,plain,
( sk_c11 = sk_c2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1802,f951]) ).
fof(f1809,plain,
( sk_c10 != multiply(sk_c11,sk_c11)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22
| spl0_50 ),
inference(superposition,[],[f1349,f1803]) ).
fof(f1810,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22
| spl0_50 ),
inference(forward_subsumption_resolution,[],[f1809,f771]) ).
fof(f1811,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22
| spl0_50 ),
inference(avatar_contradiction_clause,[],[f1810]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f175]) ).
cnf(s8,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f214]) ).
cnf(s9,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f219]) ).
cnf(s10,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f224]) ).
cnf(s11,plain,
( spl0_10
| spl0_19 ),
inference(sat_conversion,[],[f229]) ).
cnf(s18,plain,
( spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f240]) ).
cnf(s19,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f241]) ).
cnf(s20,plain,
( spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f242]) ).
cnf(s21,plain,
( spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f243]) ).
cnf(s26,plain,
( spl0_14
| spl0_21 ),
inference(sat_conversion,[],[f252]) ).
cnf(s27,plain,
( spl0_15
| spl0_21 ),
inference(sat_conversion,[],[f253]) ).
cnf(s28,plain,
( spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f254]) ).
cnf(s29,plain,
( spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f255]) ).
cnf(s30,plain,
( spl0_18
| spl0_21 ),
inference(sat_conversion,[],[f256]) ).
cnf(s31,plain,
( spl0_19
| spl0_21 ),
inference(sat_conversion,[],[f257]) ).
cnf(s36,plain,
( spl0_14
| spl0_22 ),
inference(sat_conversion,[],[f266]) ).
cnf(s37,plain,
( spl0_15
| spl0_22 ),
inference(sat_conversion,[],[f267]) ).
cnf(s38,plain,
( spl0_16
| spl0_22 ),
inference(sat_conversion,[],[f268]) ).
cnf(s39,plain,
( spl0_17
| spl0_22 ),
inference(sat_conversion,[],[f269]) ).
cnf(s40,plain,
( spl0_18
| spl0_22 ),
inference(sat_conversion,[],[f270]) ).
cnf(s41,plain,
( spl0_19
| spl0_22 ),
inference(sat_conversion,[],[f271]) ).
cnf(s46,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f276]) ).
cnf(s47,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f277]) ).
cnf(s48,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f278]) ).
cnf(s49,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f279]) ).
cnf(s50,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f280]) ).
cnf(s51,plain,
( spl0_6
| spl0_19 ),
inference(sat_conversion,[],[f281]) ).
cnf(s55,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f285]) ).
cnf(s56,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f286]) ).
cnf(s57,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f287]) ).
cnf(s58,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f288]) ).
cnf(s59,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f289]) ).
cnf(s60,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f290]) ).
cnf(s61,plain,
( spl0_7
| spl0_19 ),
inference(sat_conversion,[],[f291]) ).
cnf(s66,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f296]) ).
cnf(s67,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f297]) ).
cnf(s68,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f298]) ).
cnf(s69,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f299]) ).
cnf(s70,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f300]) ).
cnf(s71,plain,
( spl0_8
| spl0_19 ),
inference(sat_conversion,[],[f301]) ).
cnf(s72,plain,
( spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f483]) ).
cnf(s73,plain,
( spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f489]) ).
cnf(s74,plain,
( spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f529]) ).
cnf(s79,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f577]) ).
cnf(s88,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f685]) ).
cnf(s97,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f725]) ).
cnf(s100,plain,
( ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f748]) ).
cnf(s108,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f927]) ).
cnf(s113,plain,
( ~ spl0_1
| ~ spl0_22
| ~ spl0_26
| spl0_27
| ~ spl0_28 ),
inference(sat_conversion,[],[f988]) ).
cnf(s120,plain,
( ~ spl0_7
| ~ spl0_16
| ~ spl0_17
| ~ spl0_21
| spl0_28 ),
inference(sat_conversion,[],[f1073]) ).
cnf(s141,plain,
( ~ spl0_28
| spl0_44 ),
inference(sat_conversion,[],[f1246]) ).
cnf(s153,plain,
( ~ spl0_8
| ~ spl0_25
| ~ spl0_37
| spl0_42 ),
inference(sat_conversion,[],[f1300]) ).
cnf(s166,plain,
( ~ spl0_6
| ~ spl0_37
| spl0_42 ),
inference(sat_conversion,[],[f1443]) ).
cnf(s171,plain,
( ~ spl0_21
| spl0_26
| ~ spl0_37 ),
inference(sat_conversion,[],[f1469]) ).
cnf(s175,plain,
( ~ spl0_7
| ~ spl0_42
| spl0_44 ),
inference(sat_conversion,[],[f1500]) ).
cnf(s194,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_27
| ~ spl0_34
| ~ spl0_44 ),
inference(sat_conversion,[],[f1599]) ).
cnf(s195,plain,
( ~ spl0_7
| ~ spl0_8
| spl0_34
| ~ spl0_42 ),
inference(sat_conversion,[],[f1600]) ).
cnf(s200,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_25
| spl0_37 ),
inference(sat_conversion,[],[f1605]) ).
cnf(s213,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| ~ spl0_34
| spl0_37 ),
inference(sat_conversion,[],[f1632]) ).
cnf(s214,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_21
| ~ spl0_22
| spl0_28
| ~ spl0_34 ),
inference(sat_conversion,[],[f1634]) ).
cnf(s215,plain,
( ~ spl0_5
| ~ spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f1642]) ).
cnf(s221,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_20
| ~ spl0_25
| ~ spl0_34
| ~ spl0_37 ),
inference(sat_conversion,[],[f1709]) ).
cnf(s223,plain,
( ~ spl0_2
| ~ spl0_21
| ~ spl0_22
| ~ spl0_34
| ~ spl0_37 ),
inference(sat_conversion,[],[f1726]) ).
cnf(s227,plain,
( ~ spl0_3
| ~ spl0_21
| ~ spl0_22
| ~ spl0_37 ),
inference(sat_conversion,[],[f1746]) ).
cnf(s243,plain,
( ~ spl0_7
| spl0_42
| ~ spl0_44 ),
inference(sat_conversion,[],[f1764]) ).
cnf(s248,plain,
( ~ spl0_20
| spl0_25
| ~ spl0_50 ),
inference(sat_conversion,[],[f1793]) ).
cnf(s249,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_20
| ~ spl0_21
| ~ spl0_22
| spl0_50 ),
inference(sat_conversion,[],[f1811]) ).
cnf(s250,plain,
spl0_6,
inference(rat,[],[s73,s46,s47,s48,s49,s50,s51]) ).
cnf(s251,plain,
spl0_7,
inference(rat,[],[s74,s55,s56,s57,s58,s59,s60,s61]) ).
cnf(s252,plain,
spl0_8,
inference(rat,[],[s72,s66,s67,s68,s69,s70,s71]) ).
cnf(s254,plain,
( spl0_19
| ~ spl0_5 ),
inference(rat,[],[s215,s31,s41]) ).
cnf(s255,plain,
( spl0_18
| ~ spl0_5 ),
inference(rat,[],[s215,s30,s40]) ).
cnf(s256,plain,
( spl0_15
| ~ spl0_5 ),
inference(rat,[],[s215,s27,s37]) ).
cnf(s257,plain,
( ~ spl0_15
| ~ spl0_19
| ~ spl0_5
| ~ spl0_18 ),
inference(rat,[],[s215,s26,s36,s79]) ).
cnf(s258,plain,
~ spl0_5,
inference(rat,[],[s257,s256,s255,s254]) ).
cnf(s259,plain,
( ~ spl0_25
| ~ spl0_37
| ~ spl0_4
| ~ spl0_10
| ~ spl0_20 ),
inference(rat,[],[s195,s153,s221,s252,s251]) ).
cnf(s260,plain,
( spl0_19
| ~ spl0_4 ),
inference(rat,[],[s259,s200,s248,s249,s11,s21,s31,s41,s250,s252,s251]) ).
cnf(s261,plain,
( ~ spl0_20
| ~ spl0_10
| ~ spl0_22
| ~ spl0_21
| ~ spl0_4 ),
inference(rat,[],[s259,s200,s248,s249,s250,s252,s251]) ).
cnf(s262,plain,
( spl0_20
| ~ spl0_18
| ~ spl0_4 ),
inference(rat,[],[s100,s18,s19,s260]) ).
cnf(s263,plain,
( spl0_10
| ~ spl0_18
| ~ spl0_4 ),
inference(rat,[],[s100,s8,s9,s260]) ).
cnf(s264,plain,
( spl0_22
| ~ spl0_18
| ~ spl0_4 ),
inference(rat,[],[s100,s38,s39,s260]) ).
cnf(s265,plain,
( ~ spl0_18
| ~ spl0_4 ),
inference(rat,[],[s100,s28,s29,s261,s264,s263,s262,s260]) ).
cnf(s266,plain,
~ spl0_4,
inference(rat,[],[s261,s10,s20,s30,s40,s265]) ).
cnf(s267,plain,
( ~ spl0_20
| spl0_25
| ~ spl0_22
| ~ spl0_21 ),
inference(rat,[],[s248,s249,s250,s251,s252]) ).
cnf(s268,plain,
( spl0_37
| ~ spl0_22
| ~ spl0_21 ),
inference(rat,[],[s120,s18,s19,s267,s141,s243,s195,s213,s200,s250,s252,s251]) ).
cnf(s269,plain,
( ~ spl0_22
| ~ spl0_21
| ~ spl0_3 ),
inference(rat,[],[s268,s227]) ).
cnf(s270,plain,
( spl0_22
| ~ spl0_3 ),
inference(rat,[],[s97,s36,s37,s40,s41]) ).
cnf(s271,plain,
( ~ spl0_22
| ~ spl0_3 ),
inference(rat,[],[s97,s26,s27,s30,s31,s269]) ).
cnf(s272,plain,
~ spl0_3,
inference(rat,[],[s271,s270]) ).
cnf(s273,plain,
( ~ spl0_22
| ~ spl0_21
| ~ spl0_2 ),
inference(rat,[],[s195,s223,s166,s268,s251,s252,s250]) ).
cnf(s274,plain,
( spl0_22
| ~ spl0_2 ),
inference(rat,[],[s88,s38,s39,s40,s41]) ).
cnf(s275,plain,
( ~ spl0_22
| ~ spl0_2 ),
inference(rat,[],[s88,s28,s29,s30,s31,s273]) ).
cnf(s276,plain,
~ spl0_2,
inference(rat,[],[s275,s274]) ).
cnf(s277,plain,
spl0_1,
inference(rat,[],[s1,s251,s258,s266,s252,s272,s250,s276]) ).
cnf(s278,plain,
( ~ spl0_22
| ~ spl0_21 ),
inference(rat,[],[s113,s194,s214,s175,s195,s171,s166,s268,s252,s251,s250,s277]) ).
cnf(s279,plain,
spl0_22,
inference(rat,[],[s108,s38,s39,s40,s41,s251,s252,s277]) ).
cnf(s280,plain,
~ spl0_21,
inference(rat,[],[s278,s279]) ).
cnf(s281,plain,
spl0_19,
inference(rat,[],[s31,s280]) ).
cnf(s282,plain,
spl0_18,
inference(rat,[],[s30,s280]) ).
cnf(s283,plain,
spl0_17,
inference(rat,[],[s29,s280]) ).
cnf(s284,plain,
spl0_16,
inference(rat,[],[s28,s280]) ).
cnf(s291,plain,
$false,
inference(rat,[],[s108,s283,s277,s252,s251,s281,s284,s282]) ).
fof(f1813,plain,
$false,
inference(avatar_sat_refutation,[],[s291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP350-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 09:50:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 3.05/1.25 % (2298745)Input is clausal, will run a generic CNF schedule.
% 3.05/1.25 % (2298867)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2833560303:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.05/1.25 % (2298868)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=347153979:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.05/1.25 % (2298866)lrs+10_1_sil=8000:sp=occurrence:random_seed=3575924920:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.05/1.25 % (2298863)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=3843742562:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.05/1.25 % (2298864)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2457050276:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.05/1.25 % (2298865)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=192727927:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.05/1.25 % (2298866)Refutation not found, incomplete strategy
% 3.05/1.25 % (2298866)------------------------------
% 3.05/1.25 % (2298866)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.25 % (2298866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.25 % (2298866)CaDiCaL version: 2.1.3
% 3.05/1.25 % (2298866)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.25 % (2298866)Time elapsed: 0.004 s
% 3.05/1.25 % (2298866)Peak memory usage: 88 MB
% 3.05/1.25 % (2298866)Instructions burned: 6 (million)
% 3.05/1.25 % (2298867)Instruction limit reached!
% 3.05/1.25 % (2298867)------------------------------
% 3.05/1.25 % (2298867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.25 % (2298867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.25 % (2298867)CaDiCaL version: 2.1.3
% 3.05/1.25 % (2298867)Termination reason: Instruction limit
% 3.05/1.25 % (2298867)Termination phase: Saturation
% 3.05/1.25 % (2298867)Time elapsed: 0.036 s
% 3.05/1.25 % (2298867)Peak memory usage: 89 MB
% 3.05/1.25 % (2298867)Instructions burned: 116 (million)
% 3.05/1.25 % (2298869)dis-21_1_sil=8000:lcm=predicate:random_seed=1067566484: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)
% 3.05/1.25 % (2298869)Refutation not found, incomplete strategy
% 3.05/1.25 % (2298869)------------------------------
% 3.05/1.25 % (2298869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.25 % (2298869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.25 % (2298869)CaDiCaL version: 2.1.3
% 3.05/1.25 % (2298869)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.25 % (2298869)Time elapsed: 0.003 s
% 3.05/1.25 % (2298869)Peak memory usage: 88 MB
% 3.05/1.25 % (2298869)Instructions burned: 3 (million)
% 3.05/1.25 % (2298868)First to succeed.
% 3.05/1.25 % (2298868)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2298745"
% 3.05/1.25 % (2298876)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=646571224:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.05/1.25 % (2298876)Refutation not found, incomplete strategy
% 3.05/1.25 % (2298876)------------------------------
% 3.05/1.25 % (2298876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.25 % (2298876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.25 % (2298876)CaDiCaL version: 2.1.3
% 3.05/1.25 % (2298876)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.25 % (2298876)Time elapsed: 0.002 s
% 3.05/1.25 % (2298876)Peak memory usage: 88 MB
% 3.05/1.25 % (2298876)Instructions burned: 6 (million)
% 3.05/1.25 % (2298876)------------------------------
% 3.05/1.25 % (2298876)------------------------------
% 3.05/1.25 % (2298869)------------------------------
% 3.05/1.25 % (2298869)------------------------------
% 3.05/1.25 % (2298866)------------------------------
% 3.05/1.25 % (2298866)------------------------------
% 3.05/1.25 % (2298868)Refutation found. Thanks to Tanya!
% 3.05/1.25 % SZS status Unsatisfiable for theBenchmark
% 3.05/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.44 % (2298868)------------------------------
% 3.63/1.44 % (2298868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.44 % (2298868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.44 % (2298868)CaDiCaL version: 2.1.3
% 3.63/1.44 % (2298868)Termination reason: Refutation
% 3.63/1.44 % (2298868)Time elapsed: 0.037 s
% 3.63/1.44 % (2298868)Peak memory usage: 90 MB
% 3.63/1.44 % (2298868)Instructions burned: 58 (million)
% 3.63/1.44 % (2298868)------------------------------
% 3.63/1.44 % (2298868)------------------------------
% 3.63/1.44 % (2298745)Success in time 0.426 s
% 3.63/1.44 % Vampire exiting
%------------------------------------------------------------------------------