%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP307-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 10:13:36 AM UTC 2026
% Result : Unsatisfiable 2.95s 1.28s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 59
% Syntax : Number of formulae : 402 ( 22 unt; 22 def)
% Number of atoms : 1572 ( 435 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 2274 (1104 ~;1148 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c11,sk_c10) = sk_c9
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c11,sk_c10) = sk_c9
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c11,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c11,sk_c10) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c11,sk_c10) = sk_c9
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c11,sk_c10) = sk_c9
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f24,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = inverse(sk_c11)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c9 = inverse(sk_c11)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c9 = inverse(sk_c11)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c9 = inverse(sk_c11)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c9 = inverse(sk_c11)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c9 = inverse(sk_c11)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c9 = inverse(sk_c11)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c9 = inverse(sk_c11)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c11) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c9 = inverse(sk_c11)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f40]) ).
fof(f44,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f54]) ).
fof(f64,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c10 = multiply(sk_c11,sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c10 = multiply(sk_c11,sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f66]) ).
fof(f72,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c10 = multiply(sk_c11,sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c10 = multiply(sk_c11,sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f74]) ).
fof(f84,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c2
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c2 = multiply(sk_c1,sk_c11)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c2
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
( sk_c2 = multiply(sk_c1,sk_c11)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f86]) ).
fof(f92,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f93,plain,
( sk_c2 = multiply(sk_c1,sk_c11)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f92]) ).
fof(f94,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c2
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
fof(f95,plain,
( sk_c2 = multiply(sk_c1,sk_c11)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f94]) ).
fof(f104,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f105,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f104]) ).
fof(f106,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
fof(f107,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f106]) ).
fof(f112,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
fof(f113,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f112]) ).
fof(f114,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_56) ).
fof(f115,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f114]) ).
fof(f124,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(sk_c11,sk_c10) != sk_c9
| inverse(sk_c11) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(sk_c11,X0) != sk_c10
| multiply(X1,sk_c11) != X0
| 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/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
fof(f125,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(sk_c11,sk_c10) != sk_c9
| sk_c9 != inverse(sk_c11)
| sk_c11 != multiply(sk_c9,sk_c10)
| sk_c10 != multiply(sk_c11,X0)
| multiply(X1,sk_c11) != X0
| 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,[],[f124]) ).
fof(f126,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( multiply(sk_c11,sk_c10) != sk_c9
| sk_c9 != inverse(sk_c11)
| sk_c11 != multiply(sk_c9,sk_c10)
| sk_c10 != multiply(sk_c11,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(equality_resolution,[],[f125]) ).
fof(f127,plain,
! [X2,X3,X1,X6,X7,X4] :
( multiply(sk_c11,sk_c10) != sk_c9
| sk_c9 != inverse(sk_c11)
| sk_c11 != multiply(sk_c9,sk_c10)
| sk_c10 != multiply(sk_c11,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,[],[f126]) ).
fof(f128,plain,
! [X2,X3,X1,X6,X4] :
( multiply(sk_c11,sk_c10) != sk_c9
| sk_c9 != inverse(sk_c11)
| sk_c11 != multiply(sk_c9,sk_c10)
| sk_c10 != multiply(sk_c11,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,[],[f127]) ).
fof(f130,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(f131,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,[],[f130]) ).
fof(f133,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f134,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f137,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,definition,
( spl0_4
<=> ! [X1] :
( sk_c10 != multiply(sk_c11,multiply(X1,sk_c11))
| sk_c11 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f140,plain,
( ! [X1] :
( sk_c10 != multiply(sk_c11,multiply(X1,sk_c11))
| sk_c11 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,definition,
( spl0_5
<=> sk_c11 = multiply(sk_c9,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f143,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f144,plain,
( sk_c11 != multiply(sk_c9,sk_c10)
| spl0_5 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f146,definition,
( spl0_6
<=> sk_c9 = inverse(sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f147,plain,
( sk_c9 = inverse(sk_c11)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f148,plain,
( sk_c9 != inverse(sk_c11)
| spl0_6 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f150,definition,
( spl0_7
<=> multiply(sk_c11,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f151,plain,
( multiply(sk_c11,sk_c10) = sk_c9
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f152,plain,
( multiply(sk_c11,sk_c10) != sk_c9
| spl0_7 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f128,f150,f146,f142,f139,f136,f133,f130]) ).
fof(f159,definition,
( spl0_9
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f161,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f164,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f166,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f169,definition,
( spl0_11
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f171,plain,
( inverse(sk_c7) = sk_c6
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f174,definition,
( spl0_12
<=> sk_c11 = multiply(sk_c8,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f176,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f179,definition,
( spl0_13
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f181,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( spl0_13
| spl0_9 ),
inference(avatar_split_clause,[],[f115,f159,f179]) ).
fof(f184,definition,
( spl0_14
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f186,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( spl0_14
| spl0_9 ),
inference(avatar_split_clause,[],[f113,f159,f184]) ).
fof(f189,definition,
( spl0_15
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f191,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f194,definition,
( spl0_16
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f196,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f199,definition,
( spl0_17
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f201,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f202,plain,
( spl0_17
| spl0_9 ),
inference(avatar_split_clause,[],[f107,f159,f199]) ).
fof(f204,definition,
( spl0_18
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f205,plain,
( sk_c10 != multiply(sk_c3,sk_c11)
| spl0_18 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f206,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,plain,
( spl0_18
| spl0_9 ),
inference(avatar_split_clause,[],[f105,f159,f204]) ).
fof(f209,definition,
( spl0_19
<=> sk_c2 = multiply(sk_c1,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f211,plain,
( sk_c2 = multiply(sk_c1,sk_c11)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f216,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f95,f209,f179]) ).
fof(f217,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f93,f209,f184]) ).
fof(f220,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f87,f209,f199]) ).
fof(f221,plain,
( spl0_18
| spl0_19 ),
inference(avatar_split_clause,[],[f85,f209,f204]) ).
fof(f223,definition,
( spl0_20
<=> sk_c10 = multiply(sk_c11,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f225,plain,
( sk_c10 = multiply(sk_c11,sk_c2)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f230,plain,
( spl0_13
| spl0_20 ),
inference(avatar_split_clause,[],[f75,f223,f179]) ).
fof(f231,plain,
( spl0_14
| spl0_20 ),
inference(avatar_split_clause,[],[f73,f223,f184]) ).
fof(f234,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f67,f223,f199]) ).
fof(f235,plain,
( spl0_18
| spl0_20 ),
inference(avatar_split_clause,[],[f65,f223,f204]) ).
fof(f240,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f55,f142,f179]) ).
fof(f241,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f53,f142,f184]) ).
fof(f242,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f51,f142,f189]) ).
fof(f243,plain,
( spl0_16
| spl0_5 ),
inference(avatar_split_clause,[],[f49,f142,f194]) ).
fof(f244,plain,
( spl0_17
| spl0_5 ),
inference(avatar_split_clause,[],[f47,f142,f199]) ).
fof(f245,plain,
( spl0_18
| spl0_5 ),
inference(avatar_split_clause,[],[f45,f142,f204]) ).
fof(f247,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f41,f146,f164]) ).
fof(f248,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f39,f146,f169]) ).
fof(f249,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f37,f146,f174]) ).
fof(f250,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f35,f146,f179]) ).
fof(f251,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f33,f146,f184]) ).
fof(f252,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f31,f146,f189]) ).
fof(f253,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f29,f146,f194]) ).
fof(f254,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f27,f146,f199]) ).
fof(f255,plain,
( spl0_18
| spl0_6 ),
inference(avatar_split_clause,[],[f25,f146,f204]) ).
fof(f260,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f150,f179]) ).
fof(f261,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f150,f184]) ).
fof(f262,plain,
( spl0_15
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f150,f189]) ).
fof(f263,plain,
( spl0_16
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f150,f194]) ).
fof(f264,plain,
( spl0_17
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f150,f199]) ).
fof(f265,plain,
( spl0_18
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f150,f204]) ).
fof(f266,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_17 ),
inference(superposition,[],[f3,f201]) ).
fof(f267,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_15 ),
inference(superposition,[],[f3,f191]) ).
fof(f269,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f3,f171]) ).
fof(f273,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f279,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f273,f1]) ).
fof(f282,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f266]) ).
fof(f283,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_17 ),
inference(forward_demodulation,[],[f282,f1]) ).
fof(f296,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f283,f206]) ).
fof(f343,plain,
( sk_c3 = multiply(inverse(sk_c11),identity)
| ~ spl0_17 ),
inference(superposition,[],[f279,f266]) ).
fof(f345,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f279,f296]) ).
fof(f346,plain,
( sk_c4 = multiply(inverse(sk_c10),identity)
| ~ spl0_15 ),
inference(superposition,[],[f279,f267]) ).
fof(f350,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_16 ),
inference(superposition,[],[f279,f196]) ).
fof(f352,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_14 ),
inference(superposition,[],[f279,f186]) ).
fof(f361,plain,
( sk_c7 = multiply(inverse(sk_c6),identity)
| ~ spl0_11 ),
inference(superposition,[],[f279,f269]) ).
fof(f364,plain,
( sk_c7 = multiply(sk_c8,identity)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f361,f166]) ).
fof(f369,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f352,f181]) ).
fof(f371,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f350,f191]) ).
fof(f375,plain,
( identity = sk_c10
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f345,f3]) ).
fof(f377,plain,
( multiply(sk_c8,sk_c10) = sk_c7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f364,f375]) ).
fof(f378,plain,
( sk_c11 = sk_c7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f377,f176]) ).
fof(f382,plain,
( sk_c6 = inverse(sk_c11)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f171,f378]) ).
fof(f389,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f279,f369]) ).
fof(f391,plain,
( identity = sk_c11
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f389,f3]) ).
fof(f394,plain,
( sk_c11 = sk_c10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f391,f375]) ).
fof(f399,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f279,f371]) ).
fof(f401,plain,
( identity = sk_c9
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f399,f3]) ).
fof(f404,plain,
( sk_c10 = sk_c9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f401,f375]) ).
fof(f426,plain,
( sk_c4 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f346,f375]) ).
fof(f427,plain,
( identity = sk_c4
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f426,f3]) ).
fof(f428,plain,
( sk_c10 = sk_c4
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f427,f375]) ).
fof(f429,plain,
( sk_c11 = sk_c4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f428,f394]) ).
fof(f432,plain,
( multiply(sk_c11,sk_c10) = sk_c9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f196,f429]) ).
fof(f433,plain,
( sk_c10 = inverse(sk_c11)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f191,f429]) ).
fof(f434,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f433,f394]) ).
fof(f435,plain,
( $false
| spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f432,f152]) ).
fof(f436,plain,
( spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f435]) ).
fof(f443,plain,
( sk_c11 != multiply(sk_c9,sk_c11)
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f144,f394]) ).
fof(f446,plain,
( sk_c11 != multiply(sk_c10,sk_c11)
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f443,f404]) ).
fof(f449,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f446,f394]) ).
fof(f457,plain,
( sk_c11 = sk_c6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f434,f382]) ).
fof(f460,plain,
( identity = multiply(sk_c11,sk_c11)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f3,f434]) ).
fof(f461,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f460,f375]) ).
fof(f462,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f461,f394]) ).
fof(f463,plain,
( $false
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f462,f449]) ).
fof(f464,plain,
( spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f463]) ).
fof(f466,plain,
( sk_c9 != sk_c6
| spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f148,f382]) ).
fof(f468,plain,
( sk_c10 != sk_c6
| spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f466,f404]) ).
fof(f470,plain,
( sk_c11 != sk_c6
| spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f468,f394]) ).
fof(f471,plain,
( $false
| spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f457,f470]) ).
fof(f472,plain,
( spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f471]) ).
fof(f473,plain,
( ! [X2] :
( sk_c11 != inverse(X2)
| sk_c11 != multiply(X2,sk_c11) )
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f137,f394]) ).
fof(f498,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f473,f201]) ).
fof(f503,plain,
( sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f498]) ).
fof(f509,plain,
( sk_c11 != sk_c10
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f503,f206]) ).
fof(f516,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f509,f394]) ).
fof(f517,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f516]) ).
fof(f524,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_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f131,f394]) ).
fof(f637,plain,
( ! [X1] :
( sk_c11 != inverse(X1)
| sk_c11 != multiply(sk_c11,multiply(X1,sk_c11)) )
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f140,f394]) ).
fof(f646,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c11,multiply(sk_c3,sk_c11))
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f637,f201]) ).
fof(f651,plain,
( sk_c11 != multiply(sk_c11,multiply(sk_c3,sk_c11))
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f646]) ).
fof(f657,plain,
( $false
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f651,f283]) ).
fof(f658,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f657]) ).
fof(f681,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c11)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f134,f394]) ).
fof(f751,plain,
( sk_c11 = sk_c9
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f151,f296]) ).
fof(f757,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(f758,plain,
( ! [X0] :
( sk_c11 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c11) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f760,definition,
( spl0_28
<=> sk_c11 = multiply(sk_c11,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f761,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f760]) ).
fof(f762,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| spl0_28 ),
inference(avatar_component_clause,[],[f760]) ).
fof(f767,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f147,f751]) ).
fof(f769,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl0_9 ),
inference(superposition,[],[f3,f161]) ).
fof(f797,plain,
( sk_c11 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_19 ),
inference(superposition,[],[f279,f211]) ).
fof(f799,plain,
( sk_c11 = multiply(sk_c11,sk_c2)
| ~ spl0_9
| ~ spl0_19 ),
inference(forward_demodulation,[],[f797,f161]) ).
fof(f836,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != multiply(sk_c3,sk_c11)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f524,f201]) ).
fof(f848,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_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f836,f206]) ).
fof(f856,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c11,sk_c11)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f848,f394]) ).
fof(f865,plain,
( spl0_27
| ~ spl0_28
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f856,f204,f199,f184,f179,f130,f760,f757]) ).
fof(f907,plain,
( sk_c11 != inverse(sk_c11)
| sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_17
| ~ spl0_27 ),
inference(superposition,[],[f758,f201]) ).
fof(f911,plain,
( sk_c11 != inverse(sk_c11)
| sk_c11 != multiply(sk_c1,sk_c11)
| ~ spl0_9
| ~ spl0_27 ),
inference(superposition,[],[f758,f161]) ).
fof(f916,plain,
( sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f907,f767]) ).
fof(f923,plain,
( sk_c11 != sk_c10
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_demodulation,[],[f916,f206]) ).
fof(f932,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f923,f394]) ).
fof(f933,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f932]) ).
fof(f946,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c11)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f681,f751]) ).
fof(f948,plain,
( ! [X3] :
( sk_c11 != inverse(X3)
| sk_c11 != multiply(X3,sk_c11) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f946,f394]) ).
fof(f952,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f948,f201]) ).
fof(f958,plain,
( sk_c11 != multiply(sk_c3,sk_c11)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f952]) ).
fof(f964,plain,
( sk_c11 != sk_c10
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f958,f206]) ).
fof(f974,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f964,f394]) ).
fof(f975,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f974]) ).
fof(f983,plain,
( sk_c3 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f343,f391]) ).
fof(f986,plain,
( sk_c11 = multiply(sk_c11,sk_c1)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f769,f391]) ).
fof(f990,plain,
( identity = sk_c3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f983,f3]) ).
fof(f995,plain,
( sk_c11 = sk_c3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f990,f391]) ).
fof(f1009,plain,
( identity = multiply(sk_c11,sk_c11)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f266,f995]) ).
fof(f1025,plain,
( sk_c10 != multiply(sk_c11,sk_c11)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| spl0_18 ),
inference(forward_demodulation,[],[f205,f995]) ).
fof(f1026,plain,
( sk_c11 != sk_c10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| spl0_18
| ~ spl0_28 ),
inference(forward_demodulation,[],[f1025,f761]) ).
fof(f1027,plain,
( sk_c2 = multiply(inverse(sk_c11),sk_c10)
| ~ spl0_20 ),
inference(superposition,[],[f279,f225]) ).
fof(f1029,plain,
( multiply(sk_c9,sk_c10) = sk_c2
| ~ spl0_6
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1027,f147]) ).
fof(f1030,plain,
( sk_c11 = sk_c2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1029,f143]) ).
fof(f1031,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20 ),
inference(superposition,[],[f225,f1030]) ).
fof(f1032,plain,
( sk_c11 = sk_c10
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_demodulation,[],[f1031,f761]) ).
fof(f1033,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| spl0_18
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f1032,f1026]) ).
fof(f1034,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| spl0_18
| ~ spl0_20
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f1033]) ).
fof(f1035,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1009,f391]) ).
fof(f1037,plain,
( spl0_28
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1035,f199,f184,f179,f760]) ).
fof(f1046,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_9 ),
inference(superposition,[],[f131,f161]) ).
fof(f1086,definition,
( spl0_34
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f1087,plain,
( sk_c11 = sk_c9
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1091,plain,
( sk_c1 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f279,f986]) ).
fof(f1093,plain,
( identity = sk_c1
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1091,f3]) ).
fof(f1094,plain,
( sk_c11 = sk_c1
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1093,f391]) ).
fof(f1130,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f986,f1094]) ).
fof(f1132,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f161,f1094]) ).
fof(f1134,plain,
( spl0_28
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f1130,f184,f179,f159,f760]) ).
fof(f1141,plain,
( sk_c9 = multiply(sk_c11,sk_c11)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| ~ spl0_28 ),
inference(superposition,[],[f151,f1032]) ).
fof(f1146,plain,
( sk_c11 = sk_c9
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_demodulation,[],[f1141,f761]) ).
fof(f1152,plain,
( sk_c11 != sk_c9
| sk_c11 != multiply(sk_c1,sk_c11)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_27 ),
inference(forward_demodulation,[],[f911,f147]) ).
fof(f1153,plain,
( spl0_34
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f1146,f760,f223,f150,f146,f142,f1086]) ).
fof(f1168,plain,
( sk_c11 != sk_c2
| sk_c11 != sk_c9
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1152,f211]) ).
fof(f1169,plain,
( sk_c11 != sk_c9
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1168,f1030]) ).
fof(f1170,plain,
( ~ spl0_34
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f1169,f757,f223,f209,f159,f146,f142,f1086]) ).
fof(f1171,plain,
( ! [X2] :
( sk_c11 != inverse(X2)
| sk_c11 != multiply(X2,sk_c11) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_demodulation,[],[f137,f1032]) ).
fof(f1172,plain,
( sk_c11 != sk_c9
| sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28 ),
inference(superposition,[],[f1171,f147]) ).
fof(f1182,plain,
( sk_c11 != sk_c9
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f1172,f761]) ).
fof(f1186,plain,
( ~ spl0_34
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f1182,f760,f223,f146,f142,f136,f1086]) ).
fof(f1187,plain,
( ! [X1] :
( sk_c11 != inverse(X1)
| sk_c11 != multiply(sk_c11,multiply(X1,sk_c11)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_demodulation,[],[f140,f1032]) ).
fof(f1194,plain,
( sk_c11 != sk_c9
| sk_c11 != multiply(sk_c11,multiply(sk_c11,sk_c11))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28 ),
inference(superposition,[],[f1187,f147]) ).
fof(f1199,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c11,multiply(sk_c1,sk_c11))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_20
| ~ spl0_28 ),
inference(superposition,[],[f1187,f161]) ).
fof(f1200,plain,
( sk_c11 != multiply(sk_c11,multiply(sk_c1,sk_c11))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_20
| ~ spl0_28 ),
inference(trivial_inequality_removal,[],[f1199]) ).
fof(f1201,plain,
( sk_c11 != multiply(sk_c11,sk_c2)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_demodulation,[],[f1200,f211]) ).
fof(f1204,plain,
( sk_c11 != multiply(sk_c11,multiply(sk_c11,sk_c11))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f1194,f1087]) ).
fof(f1205,plain,
( sk_c11 != sk_c10
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_demodulation,[],[f1201,f225]) ).
fof(f1212,plain,
( sk_c11 != multiply(sk_c11,sk_c11)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1204,f761]) ).
fof(f1213,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f1205,f1032]) ).
fof(f1214,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f1213]) ).
fof(f1216,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f1212,f761]) ).
fof(f1217,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(avatar_contradiction_clause,[],[f1216]) ).
fof(f1218,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c11)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_demodulation,[],[f134,f1032]) ).
fof(f1219,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c11)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1218,f1087]) ).
fof(f1220,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1219,f1032]) ).
fof(f1230,plain,
( identity != sk_c11
| sk_c11 != inverse(inverse(sk_c11))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(superposition,[],[f1220,f3]) ).
fof(f1233,plain,
( sk_c11 != sk_c2
| sk_c11 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(superposition,[],[f1220,f211]) ).
fof(f1236,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f1233,f1030]) ).
fof(f1239,plain,
( sk_c11 != inverse(inverse(sk_c11))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f1230,f391]) ).
fof(f1241,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f1236,f161]) ).
fof(f1242,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(avatar_contradiction_clause,[],[f1241]) ).
fof(f1243,plain,
( sk_c11 != inverse(sk_c9)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1239,f147]) ).
fof(f1246,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1243,f1087]) ).
fof(f1247,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f1246,f1132]) ).
fof(f1248,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(avatar_contradiction_clause,[],[f1247]) ).
fof(f1255,plain,
( ! [X0] :
( sk_c11 != sk_c9
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0))
| sk_c11 != multiply(sk_c1,sk_c11) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1046,f151]) ).
fof(f1277,plain,
( ! [X0] :
( sk_c11 != sk_c2
| sk_c11 != sk_c9
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1255,f211]) ).
fof(f1280,plain,
( ! [X0] :
( sk_c11 != sk_c9
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f1277,f1030]) ).
fof(f1282,plain,
( spl0_27
| ~ spl0_34
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1280,f223,f209,f159,f150,f146,f142,f130,f1086,f757]) ).
fof(f1304,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f799,f1030]) ).
fof(f1305,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f1304,f762]) ).
fof(f1306,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| spl0_28 ),
inference(avatar_contradiction_clause,[],[f1305]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f153]) ).
cnf(s6,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f182]) ).
cnf(s7,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f187]) ).
cnf(s10,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f202]) ).
cnf(s11,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f207]) ).
cnf(s16,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f216]) ).
cnf(s17,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f217]) ).
cnf(s20,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f220]) ).
cnf(s21,plain,
( spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f221]) ).
cnf(s26,plain,
( spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f230]) ).
cnf(s27,plain,
( spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f231]) ).
cnf(s30,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f234]) ).
cnf(s31,plain,
( spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f235]) ).
cnf(s36,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f240]) ).
cnf(s37,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f241]) ).
cnf(s38,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f242]) ).
cnf(s39,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f243]) ).
cnf(s40,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f244]) ).
cnf(s41,plain,
( spl0_5
| spl0_18 ),
inference(sat_conversion,[],[f245]) ).
cnf(s43,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f247]) ).
cnf(s44,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f248]) ).
cnf(s45,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f249]) ).
cnf(s46,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f250]) ).
cnf(s47,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f251]) ).
cnf(s48,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f252]) ).
cnf(s49,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f253]) ).
cnf(s50,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f254]) ).
cnf(s51,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f255]) ).
cnf(s56,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f260]) ).
cnf(s57,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f261]) ).
cnf(s58,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f262]) ).
cnf(s59,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f263]) ).
cnf(s60,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f264]) ).
cnf(s61,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f265]) ).
cnf(s62,plain,
( spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f436]) ).
cnf(s63,plain,
( spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f464]) ).
cnf(s64,plain,
( spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f472]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f517]) ).
cnf(s77,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f658]) ).
cnf(s111,plain,
( ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| spl0_27
| ~ spl0_28 ),
inference(sat_conversion,[],[f865]) ).
cnf(s120,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_27 ),
inference(sat_conversion,[],[f933]) ).
cnf(s128,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f975]) ).
cnf(s135,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| spl0_18
| ~ spl0_20
| ~ spl0_28 ),
inference(sat_conversion,[],[f1034]) ).
cnf(s136,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| spl0_28 ),
inference(sat_conversion,[],[f1037]) ).
cnf(s148,plain,
( ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| spl0_28 ),
inference(sat_conversion,[],[f1134]) ).
cnf(s151,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| ~ spl0_28
| spl0_34 ),
inference(sat_conversion,[],[f1153]) ).
cnf(s154,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_27
| ~ spl0_34 ),
inference(sat_conversion,[],[f1170]) ).
cnf(s156,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(sat_conversion,[],[f1186]) ).
cnf(s159,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28 ),
inference(sat_conversion,[],[f1214]) ).
cnf(s161,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(sat_conversion,[],[f1217]) ).
cnf(s163,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(sat_conversion,[],[f1242]) ).
cnf(s165,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_28
| ~ spl0_34 ),
inference(sat_conversion,[],[f1248]) ).
cnf(s175,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| spl0_27
| ~ spl0_34 ),
inference(sat_conversion,[],[f1282]) ).
cnf(s179,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| spl0_28 ),
inference(sat_conversion,[],[f1306]) ).
cnf(s180,plain,
spl0_5,
inference(rat,[],[s63,s36,s37,s38,s39,s40,s41]) ).
cnf(s181,plain,
spl0_6,
inference(rat,[],[s64,s43,s44,s45,s46,s47,s48,s49,s50,s51]) ).
cnf(s182,plain,
spl0_7,
inference(rat,[],[s62,s56,s57,s58,s59,s60,s61]) ).
cnf(s183,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s77,s6,s7,s10,s11]) ).
cnf(s184,plain,
( ~ spl0_17
| ~ spl0_14
| ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s135,s31,s77,s148,s183,s180,s181]) ).
cnf(s185,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s161,s151,s30,s184,s148,s183,s180,s181,s182]) ).
cnf(s186,plain,
( spl0_14
| ~ spl0_4 ),
inference(rat,[],[s159,s179,s17,s27,s183,s180,s181]) ).
cnf(s187,plain,
~ spl0_4,
inference(rat,[],[s159,s179,s16,s26,s185,s186,s183,s180,s181]) ).
cnf(s188,plain,
( ~ spl0_28
| ~ spl0_20
| ~ spl0_3 ),
inference(rat,[],[s156,s151,s180,s181,s182]) ).
cnf(s189,plain,
( spl0_28
| ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s10,s148,s136]) ).
cnf(s190,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_3 ),
inference(rat,[],[s66,s30,s31,s188,s189]) ).
cnf(s191,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s179,s188,s7,s17,s27,s180,s181]) ).
cnf(s192,plain,
( ~ spl0_14
| ~ spl0_3 ),
inference(rat,[],[s179,s188,s6,s16,s26,s190,s181,s180]) ).
cnf(s193,plain,
~ spl0_3,
inference(rat,[],[s192,s191]) ).
cnf(s194,plain,
( spl0_9
| ~ spl0_14
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s128,s10,s11,s182]) ).
cnf(s195,plain,
( ~ spl0_20
| ~ spl0_14
| ~ spl0_13
| ~ spl0_28
| ~ spl0_2 ),
inference(rat,[],[s165,s151,s194,s180,s181,s182]) ).
cnf(s196,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_2
| ~ spl0_28 ),
inference(rat,[],[s128,s30,s31,s195,s182]) ).
cnf(s197,plain,
( spl0_14
| ~ spl0_28
| ~ spl0_2 ),
inference(rat,[],[s163,s151,s7,s17,s27,s180,s181,s182]) ).
cnf(s198,plain,
( ~ spl0_14
| ~ spl0_28
| ~ spl0_2 ),
inference(rat,[],[s163,s151,s6,s16,s26,s196,s182,s181,s180]) ).
cnf(s199,plain,
( ~ spl0_28
| ~ spl0_2 ),
inference(rat,[],[s198,s197]) ).
cnf(s200,plain,
( spl0_13
| spl0_28 ),
inference(rat,[],[s179,s6,s16,s26,s180,s181]) ).
cnf(s201,plain,
( ~ spl0_13
| spl0_28 ),
inference(rat,[],[s179,s7,s17,s27,s189,s181,s180]) ).
cnf(s202,plain,
spl0_28,
inference(rat,[],[s201,s200]) ).
cnf(s203,plain,
~ spl0_2,
inference(rat,[],[s199,s202]) ).
cnf(s204,plain,
spl0_1,
inference(rat,[],[s1,s181,s180,s187,s182,s193,s203]) ).
cnf(s205,plain,
( ~ spl0_19
| ~ spl0_9
| ~ spl0_34
| ~ spl0_20 ),
inference(rat,[],[s154,s175,s182,s204,s181,s180]) ).
cnf(s206,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s120,s111,s202,s204,s182,s181]) ).
cnf(s207,plain,
( spl0_19
| ~ spl0_13
| ~ spl0_14 ),
inference(rat,[],[s206,s20,s21]) ).
cnf(s208,plain,
( spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(rat,[],[s206,s10,s11]) ).
cnf(s209,plain,
( ~ spl0_20
| ~ spl0_9
| ~ spl0_19 ),
inference(rat,[],[s205,s151,s180,s181,s182,s202]) ).
cnf(s210,plain,
( ~ spl0_13
| ~ spl0_14 ),
inference(rat,[],[s206,s30,s31,s209,s208,s207]) ).
cnf(s211,plain,
spl0_13,
inference(rat,[],[s205,s151,s6,s16,s26,s180,s181,s182,s202]) ).
cnf(s212,plain,
~ spl0_14,
inference(rat,[],[s210,s211]) ).
cnf(s213,plain,
spl0_20,
inference(rat,[],[s27,s212]) ).
cnf(s214,plain,
spl0_19,
inference(rat,[],[s17,s212]) ).
cnf(s215,plain,
spl0_9,
inference(rat,[],[s7,s212]) ).
cnf(s216,plain,
spl0_34,
inference(rat,[],[s151,s202,s182,s181,s180,s213]) ).
cnf(s218,plain,
$false,
inference(rat,[],[s205,s215,s214,s213,s216]) ).
fof(f1307,plain,
$false,
inference(avatar_sat_refutation,[],[s218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP307-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:55:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.95/1.28 % (3313983)Input is clausal, will run a generic CNF schedule.
% 2.95/1.28 % (3313992)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=524015563:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.95/1.28 % (3313992)Instruction limit reached!
% 2.95/1.28 % (3313992)------------------------------
% 2.95/1.28 % (3313992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.28 % (3313992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.28 % (3313992)CaDiCaL version: 2.1.3
% 2.95/1.28 % (3313992)Termination reason: Instruction limit
% 2.95/1.28 % (3313992)Termination phase: Saturation
% 2.95/1.28 % (3313992)Time elapsed: 0.036 s
% 2.95/1.28 % (3313992)Peak memory usage: 89 MB
% 2.95/1.28 % (3313992)Instructions burned: 117 (million)
% 2.95/1.28 % (3313989)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1487906245:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.95/1.28 % (3313988)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=3312523580:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.95/1.28 % (3313990)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2666858983:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.95/1.28 % (3313991)lrs+10_1_sil=8000:sp=occurrence:random_seed=3181186126:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.95/1.28 % (3313993)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1489982608:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.95/1.28 % (3313994)dis-21_1_sil=8000:lcm=predicate:random_seed=4282702986: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)
% 2.95/1.28 % (3313991)Refutation not found, incomplete strategy
% 2.95/1.28 % (3313991)------------------------------
% 2.95/1.28 % (3313991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.28 % (3313991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.28 % (3313991)CaDiCaL version: 2.1.3
% 2.95/1.28 % (3313991)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.28 % (3313991)Time elapsed: 0.004 s
% 2.95/1.28 % (3313991)Peak memory usage: 88 MB
% 2.95/1.28 % (3313991)Instructions burned: 6 (million)
% 2.95/1.28 % (3313994)Refutation not found, incomplete strategy
% 2.95/1.28 % (3313994)------------------------------
% 2.95/1.28 % (3313994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.28 % (3313994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.28 % (3313994)CaDiCaL version: 2.1.3
% 2.95/1.28 % (3313994)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.28 % (3313994)Time elapsed: 0.002 s
% 2.95/1.28 % (3313994)Peak memory usage: 88 MB
% 2.95/1.28 % (3313994)Instructions burned: 3 (million)
% 2.95/1.28 % (3313993)First to succeed.
% 2.95/1.28 % (3313993)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3313983"
% 2.95/1.28 % (3313996)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=3349070317:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.95/1.28 % (3313996)Refutation not found, incomplete strategy
% 2.95/1.28 % (3313996)------------------------------
% 2.95/1.28 % (3313996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.28 % (3313996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.28 % (3313996)CaDiCaL version: 2.1.3
% 2.95/1.28 % (3313996)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.28 % (3313996)Time elapsed: 0.002 s
% 2.95/1.28 % (3313996)Peak memory usage: 88 MB
% 2.95/1.28 % (3313996)Instructions burned: 6 (million)
% 2.95/1.28 % (3313996)------------------------------
% 2.95/1.28 % (3313996)------------------------------
% 2.95/1.28 % (3313994)------------------------------
% 2.95/1.28 % (3313994)------------------------------
% 2.95/1.28 % (3313991)------------------------------
% 2.95/1.28 % (3313991)------------------------------
% 2.95/1.28 % (3313993)Refutation found. Thanks to Tanya!
% 2.95/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.95/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.48 % (3313993)------------------------------
% 3.69/1.48 % (3313993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.48 % (3313993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.48 % (3313993)CaDiCaL version: 2.1.3
% 3.69/1.48 % (3313993)Termination reason: Refutation
% 3.69/1.48 % (3313993)Time elapsed: 0.030 s
% 3.69/1.48 % (3313993)Peak memory usage: 90 MB
% 3.69/1.48 % (3313993)Instructions burned: 42 (million)
% 3.69/1.48 % (3313993)------------------------------
% 3.69/1.48 % (3313993)------------------------------
% 3.69/1.48 % (3313983)Success in time 0.441 s
% 3.69/1.48 % Vampire exiting
%------------------------------------------------------------------------------