%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP384-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 10:17:39 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 56
% Syntax : Number of formulae : 411 ( 19 unt; 22 def)
% Number of atoms : 1604 ( 474 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 2346 (1153 ~;1171 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 97 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c11) = sk_c10
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f12,negated_conjecture,
( inverse(sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c11) = sk_c10
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c11) = sk_c10
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f14]) ).
fof(f23,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f63,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f71,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f83,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c2 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f91,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c2 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f93]) ).
fof(f103,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_51) ).
fof(f104,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f103]) ).
fof(f105,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
fof(f106,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f105]) ).
fof(f107,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_53) ).
fof(f108,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f107]) ).
fof(f109,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
fof(f110,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f109]) ).
fof(f111,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
fof(f112,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f111]) ).
fof(f113,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
fof(f114,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f113]) ).
fof(f123,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X0,X1) != sk_c10
| inverse(X0) != X1
| 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_61) ).
fof(f124,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(sk_c10,sk_c9)
| sk_c10 != multiply(sk_c11,sk_c9)
| multiply(X0,X1) != sk_c10
| inverse(X0) != 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,[],[f123]) ).
fof(f125,plain,
! [X2,X3,X0,X6,X7,X4,X5] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(sk_c10,sk_c9)
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),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(equality_resolution,[],[f124]) ).
fof(f126,plain,
! [X2,X3,X0,X6,X7,X4] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(sk_c10,sk_c9)
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),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,[],[f125]) ).
fof(f127,plain,
! [X2,X3,X0,X6,X4] :
( inverse(sk_c11) != sk_c10
| sk_c11 != multiply(sk_c10,sk_c9)
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),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,[],[f126]) ).
fof(f129,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(f130,plain,
( ! [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) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f133,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f136,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,definition,
( spl0_4
<=> ! [X0] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f139,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != multiply(X0,inverse(X0)) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f141,definition,
( spl0_5
<=> sk_c10 = multiply(sk_c11,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f142,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f143,plain,
( sk_c10 != multiply(sk_c11,sk_c9)
| spl0_5 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f145,definition,
( spl0_6
<=> sk_c11 = multiply(sk_c10,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f146,plain,
( sk_c11 = multiply(sk_c10,sk_c9)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f147,plain,
( sk_c11 != multiply(sk_c10,sk_c9)
| spl0_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f149,definition,
( spl0_7
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f150,plain,
( inverse(sk_c11) = sk_c10
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f151,plain,
( inverse(sk_c11) != sk_c10
| spl0_7 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f127,f149,f145,f141,f138,f135,f132,f129]) ).
fof(f158,definition,
( spl0_9
<=> sk_c10 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f160,plain,
( sk_c10 = multiply(sk_c2,sk_c9)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f178,definition,
( spl0_13
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f180,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f181,plain,
( spl0_13
| spl0_9 ),
inference(avatar_split_clause,[],[f114,f158,f178]) ).
fof(f183,definition,
( spl0_14
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f185,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f186,plain,
( spl0_14
| spl0_9 ),
inference(avatar_split_clause,[],[f112,f158,f183]) ).
fof(f188,definition,
( spl0_15
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f190,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f191,plain,
( spl0_15
| spl0_9 ),
inference(avatar_split_clause,[],[f110,f158,f188]) ).
fof(f193,definition,
( spl0_16
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f195,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f196,plain,
( spl0_16
| spl0_9 ),
inference(avatar_split_clause,[],[f108,f158,f193]) ).
fof(f198,definition,
( spl0_17
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f200,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f201,plain,
( spl0_17
| spl0_9 ),
inference(avatar_split_clause,[],[f106,f158,f198]) ).
fof(f203,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,[],[f203]) ).
fof(f206,plain,
( spl0_18
| spl0_9 ),
inference(avatar_split_clause,[],[f104,f158,f203]) ).
fof(f208,definition,
( spl0_19
<=> sk_c2 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f210,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f215,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f94,f208,f178]) ).
fof(f216,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f92,f208,f183]) ).
fof(f219,plain,
( spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f86,f208,f198]) ).
fof(f220,plain,
( spl0_18
| spl0_19 ),
inference(avatar_split_clause,[],[f84,f208,f203]) ).
fof(f222,definition,
( spl0_20
<=> sk_c10 = multiply(sk_c1,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f224,plain,
( sk_c10 = multiply(sk_c1,sk_c2)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f229,plain,
( spl0_13
| spl0_20 ),
inference(avatar_split_clause,[],[f74,f222,f178]) ).
fof(f230,plain,
( spl0_14
| spl0_20 ),
inference(avatar_split_clause,[],[f72,f222,f183]) ).
fof(f233,plain,
( spl0_17
| spl0_20 ),
inference(avatar_split_clause,[],[f66,f222,f198]) ).
fof(f234,plain,
( spl0_18
| spl0_20 ),
inference(avatar_split_clause,[],[f64,f222,f203]) ).
fof(f239,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f54,f141,f178]) ).
fof(f240,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f52,f141,f183]) ).
fof(f241,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f50,f141,f188]) ).
fof(f242,plain,
( spl0_16
| spl0_5 ),
inference(avatar_split_clause,[],[f48,f141,f193]) ).
fof(f243,plain,
( spl0_17
| spl0_5 ),
inference(avatar_split_clause,[],[f46,f141,f198]) ).
fof(f244,plain,
( spl0_18
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f141,f203]) ).
fof(f249,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f34,f145,f178]) ).
fof(f250,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f32,f145,f183]) ).
fof(f251,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f30,f145,f188]) ).
fof(f252,plain,
( spl0_16
| spl0_6 ),
inference(avatar_split_clause,[],[f28,f145,f193]) ).
fof(f253,plain,
( spl0_17
| spl0_6 ),
inference(avatar_split_clause,[],[f26,f145,f198]) ).
fof(f254,plain,
( spl0_18
| spl0_6 ),
inference(avatar_split_clause,[],[f24,f145,f203]) ).
fof(f259,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f15,f149,f178]) ).
fof(f260,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f13,f149,f183]) ).
fof(f263,plain,
( spl0_17
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f149,f198]) ).
fof(f264,plain,
( spl0_18
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f149,f203]) ).
fof(f265,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_17 ),
inference(superposition,[],[f3,f200]) ).
fof(f272,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f278,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f272,f1]) ).
fof(f281,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f265]) ).
fof(f282,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_17 ),
inference(forward_demodulation,[],[f281,f1]) ).
fof(f295,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f282,f205]) ).
fof(f342,plain,
( sk_c3 = multiply(inverse(sk_c11),identity)
| ~ spl0_17 ),
inference(superposition,[],[f278,f265]) ).
fof(f344,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f278,f295]) ).
fof(f349,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_16 ),
inference(superposition,[],[f278,f195]) ).
fof(f352,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_14 ),
inference(superposition,[],[f278,f185]) ).
fof(f369,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f352,f180]) ).
fof(f372,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f349,f190]) ).
fof(f376,plain,
( identity = sk_c10
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f344,f3]) ).
fof(f409,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f278,f369]) ).
fof(f411,plain,
( identity = sk_c11
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f409,f3]) ).
fof(f414,plain,
( sk_c10 != inverse(identity)
| spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f151,f411]) ).
fof(f427,plain,
( identity != inverse(identity)
| spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f414,f376]) ).
fof(f430,plain,
( identity = multiply(identity,sk_c9)
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f372,f376]) ).
fof(f431,plain,
( identity = sk_c9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f430,f1]) ).
fof(f434,plain,
( sk_c3 = multiply(inverse(identity),identity)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f342,f411]) ).
fof(f435,plain,
( identity = sk_c3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f434,f3]) ).
fof(f440,plain,
( sk_c11 = inverse(identity)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f200,f435]) ).
fof(f441,plain,
( identity = inverse(identity)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f440,f411]) ).
fof(f539,plain,
( $false
| spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f427,f441]) ).
fof(f540,plain,
( spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f539]) ).
fof(f541,plain,
( sk_c10 != multiply(sk_c11,identity)
| spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f143,f431]) ).
fof(f542,plain,
( identity = inverse(sk_c11)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f150,f376]) ).
fof(f543,plain,
( sk_c10 != multiply(identity,identity)
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f541,f411]) ).
fof(f545,plain,
( identity != sk_c10
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f543,f1]) ).
fof(f546,plain,
( $false
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f545,f376]) ).
fof(f547,plain,
( spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f546]) ).
fof(f549,plain,
( sk_c11 != multiply(sk_c10,identity)
| spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f147,f431]) ).
fof(f551,plain,
( sk_c11 != multiply(identity,identity)
| spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f549,f376]) ).
fof(f553,plain,
( identity != sk_c11
| spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f551,f1]) ).
fof(f554,plain,
( $false
| spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f553,f411]) ).
fof(f555,plain,
( spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f554]) ).
fof(f556,plain,
( ! [X2] :
( sk_c10 != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f136,f411]) ).
fof(f558,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f556,f376]) ).
fof(f560,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f558,f411]) ).
fof(f564,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f560,f3]) ).
fof(f569,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f564]) ).
fof(f574,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f569,f441]) ).
fof(f580,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f574,f441]) ).
fof(f581,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f580]) ).
fof(f589,plain,
( ! [X0] :
( identity != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f139,f376]) ).
fof(f590,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f589,f431]) ).
fof(f591,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f590,f376]) ).
fof(f595,plain,
( identity != multiply(sk_c10,identity)
| identity != multiply(sk_c4,sk_c10)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f591,f190]) ).
fof(f611,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c4,sk_c10)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f595,f376]) ).
fof(f622,plain,
( identity != multiply(sk_c4,sk_c10)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f611,f1]) ).
fof(f630,plain,
( identity != sk_c9
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f622,f195]) ).
fof(f638,plain,
( $false
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f630,f431]) ).
fof(f639,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f638]) ).
fof(f649,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f133,f376]) ).
fof(f778,plain,
( identity = multiply(sk_c1,sk_c2)
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(forward_demodulation,[],[f224,f376]) ).
fof(f819,definition,
( spl0_26
<=> identity = multiply(sk_c2,identity) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f820,plain,
( identity = multiply(sk_c2,identity)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f819]) ).
fof(f823,definition,
( spl0_27
<=> identity = multiply(sk_c1,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f824,plain,
( identity = multiply(sk_c1,sk_c2)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f825,plain,
( identity != multiply(sk_c1,sk_c2)
| spl0_27 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f830,plain,
( spl0_27
| ~ spl0_17
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f778,f222,f203,f198,f823]) ).
fof(f855,plain,
( sk_c2 = multiply(inverse(sk_c1),identity)
| ~ spl0_27 ),
inference(superposition,[],[f278,f824]) ).
fof(f858,plain,
( sk_c2 = multiply(sk_c2,identity)
| ~ spl0_19
| ~ spl0_27 ),
inference(forward_demodulation,[],[f855,f210]) ).
fof(f859,plain,
( identity = sk_c2
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f858,f820]) ).
fof(f901,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f142,f411]) ).
fof(f902,plain,
( sk_c11 = multiply(identity,sk_c9)
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f146,f376]) ).
fof(f904,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_9
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f160,f859]) ).
fof(f906,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f901,f1]) ).
fof(f907,plain,
( sk_c11 = sk_c9
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f902,f1]) ).
fof(f909,plain,
( sk_c10 = sk_c9
| ~ spl0_9
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f904,f1]) ).
fof(f911,plain,
( identity = sk_c9
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f906,f376]) ).
fof(f914,plain,
( identity = sk_c9
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f909,f376]) ).
fof(f946,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f649,f911]) ).
fof(f948,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f946,f376]) ).
fof(f953,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f948,f3]) ).
fof(f957,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f953]) ).
fof(f969,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f957,f441]) ).
fof(f974,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f969,f441]) ).
fof(f975,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f974]) ).
fof(f1014,plain,
( identity = sk_c11
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(superposition,[],[f914,f907]) ).
fof(f1028,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f542,f1014]) ).
fof(f1069,plain,
( ! [X3] :
( sk_c11 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f649,f907]) ).
fof(f1072,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1069,f1014]) ).
fof(f1075,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1072,f376]) ).
fof(f1081,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(superposition,[],[f1075,f3]) ).
fof(f1085,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f1081]) ).
fof(f1089,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1085,f1028]) ).
fof(f1094,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1089,f1028]) ).
fof(f1095,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1094]) ).
fof(f1099,plain,
( sk_c10 = multiply(sk_c2,sk_c11)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f160,f907]) ).
fof(f1101,plain,
( identity = multiply(sk_c2,sk_c11)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1099,f376]) ).
fof(f1103,plain,
( identity = multiply(identity,sk_c11)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f3,f542]) ).
fof(f1104,plain,
( identity = sk_c11
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1103,f1]) ).
fof(f1111,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f542,f1104]) ).
fof(f1138,plain,
( identity = multiply(sk_c2,identity)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1101,f1104]) ).
fof(f1139,plain,
( spl0_26
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f1138,f203,f198,f158,f149,f145,f819]) ).
fof(f1141,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),sk_c11)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f589,f907]) ).
fof(f1148,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1141,f1104]) ).
fof(f1152,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1148,f376]) ).
fof(f1168,plain,
( identity != multiply(sk_c11,identity)
| identity != multiply(sk_c3,sk_c11)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f1152,f200]) ).
fof(f1179,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c3,sk_c11)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1168,f1104]) ).
fof(f1186,plain,
( identity != multiply(sk_c3,sk_c11)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1179,f1]) ).
fof(f1190,plain,
( identity != sk_c10
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1186,f205]) ).
fof(f1193,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1190,f376]) ).
fof(f1194,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1193]) ).
fof(f1195,plain,
( ! [X6,X4] :
( identity != 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_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f130,f1104]) ).
fof(f1196,plain,
( ! [X6,X4] :
( sk_c11 != multiply(inverse(X4),identity)
| identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1195,f376]) ).
fof(f1197,plain,
( ! [X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| identity != multiply(X4,inverse(X4))
| identity != multiply(inverse(X4),identity)
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1196,f1104]) ).
fof(f1200,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f1197,f542]) ).
fof(f1212,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1200,f1]) ).
fof(f1217,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1212,f1104]) ).
fof(f1222,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1217,f1]) ).
fof(f1234,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f1222,f3]) ).
fof(f1237,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1234,f1111]) ).
fof(f1239,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1237,f1111]) ).
fof(f1241,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1239,f1111]) ).
fof(f1244,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1241,f1111]) ).
fof(f1245,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1244,f1111]) ).
fof(f1246,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1245]) ).
fof(f1247,plain,
( identity = sk_c10
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_demodulation,[],[f224,f824]) ).
fof(f1251,plain,
( identity = inverse(sk_c11)
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_demodulation,[],[f150,f1247]) ).
fof(f1253,plain,
( identity = multiply(identity,sk_c11)
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(superposition,[],[f3,f1251]) ).
fof(f1254,plain,
( identity = sk_c11
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1253,f1]) ).
fof(f1258,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(superposition,[],[f1251,f1254]) ).
fof(f1275,plain,
( ! [X2] :
( sk_c10 != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_demodulation,[],[f136,f1254]) ).
fof(f1276,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1275,f1247]) ).
fof(f1277,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1276,f1254]) ).
fof(f1283,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(superposition,[],[f1277,f3]) ).
fof(f1286,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f1283]) ).
fof(f1288,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1286,f1258]) ).
fof(f1291,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1288,f1258]) ).
fof(f1292,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1291]) ).
fof(f1294,plain,
( identity = multiply(sk_c10,sk_c11)
| ~ spl0_7 ),
inference(superposition,[],[f3,f150]) ).
fof(f1296,plain,
( sk_c9 = multiply(inverse(sk_c11),sk_c10)
| ~ spl0_5 ),
inference(superposition,[],[f278,f142]) ).
fof(f1298,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1296,f150]) ).
fof(f1303,plain,
( sk_c2 = multiply(inverse(sk_c1),sk_c10)
| ~ spl0_20 ),
inference(superposition,[],[f278,f224]) ).
fof(f1305,plain,
( sk_c2 = multiply(sk_c2,sk_c10)
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1303,f210]) ).
fof(f1316,definition,
( spl0_38
<=> sk_c11 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f1317,plain,
( sk_c11 = inverse(identity)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f1318,plain,
( sk_c11 != inverse(identity)
| spl0_38 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f1320,definition,
( spl0_39
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f1321,plain,
( sk_c11 = sk_c10
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f1320]) ).
fof(f1322,plain,
( sk_c11 != sk_c10
| spl0_39 ),
inference(avatar_component_clause,[],[f1320]) ).
fof(f1325,definition,
( spl0_40
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f1326,plain,
( identity = sk_c10
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f1325]) ).
fof(f1329,definition,
( spl0_41
<=> sk_c11 = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f1330,plain,
( sk_c11 = inverse(sk_c10)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1329]) ).
fof(f1331,plain,
( sk_c11 != inverse(sk_c10)
| spl0_41 ),
inference(avatar_component_clause,[],[f1329]) ).
fof(f1333,plain,
( identity != sk_c10
| ~ spl0_20
| spl0_27 ),
inference(forward_demodulation,[],[f825,f224]) ).
fof(f1334,plain,
( ~ spl0_40
| ~ spl0_20
| spl0_27 ),
inference(avatar_split_clause,[],[f1333,f823,f222,f1325]) ).
fof(f1394,plain,
( identity = multiply(sk_c11,sk_c11)
| ~ spl0_7
| ~ spl0_39 ),
inference(superposition,[],[f1294,f1321]) ).
fof(f1396,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_39
| spl0_41 ),
inference(superposition,[],[f1331,f1321]) ).
fof(f1398,plain,
( sk_c11 != sk_c10
| ~ spl0_7
| ~ spl0_39
| spl0_41 ),
inference(forward_demodulation,[],[f1396,f150]) ).
fof(f1401,plain,
( $false
| ~ spl0_7
| ~ spl0_39
| spl0_41 ),
inference(forward_subsumption_resolution,[],[f1398,f1321]) ).
fof(f1402,plain,
( ~ spl0_7
| ~ spl0_39
| spl0_41 ),
inference(avatar_contradiction_clause,[],[f1401]) ).
fof(f1414,plain,
( sk_c9 = multiply(sk_c11,sk_c11)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_39 ),
inference(forward_demodulation,[],[f1298,f1321]) ).
fof(f1519,plain,
( identity = sk_c9
| ~ spl0_5
| ~ spl0_7
| ~ spl0_39 ),
inference(forward_demodulation,[],[f1414,f1394]) ).
fof(f1522,plain,
( sk_c10 = multiply(sk_c2,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_39 ),
inference(superposition,[],[f160,f1519]) ).
fof(f1527,plain,
( sk_c11 = multiply(sk_c2,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_39 ),
inference(forward_demodulation,[],[f1522,f1321]) ).
fof(f1551,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c2)
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f278,f1305]) ).
fof(f1553,plain,
( identity = sk_c10
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1551,f3]) ).
fof(f1557,plain,
( spl0_40
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1553,f222,f208,f1325]) ).
fof(f1579,plain,
( sk_c10 != multiply(sk_c2,sk_c9)
| sk_c10 != multiply(sk_c1,sk_c2)
| ~ spl0_4
| ~ spl0_19 ),
inference(superposition,[],[f139,f210]) ).
fof(f1586,plain,
( sk_c10 != multiply(sk_c1,sk_c2)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1579,f160]) ).
fof(f1599,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f1586,f224]) ).
fof(f1600,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f1599]) ).
fof(f1616,plain,
( identity != sk_c11
| spl0_39
| ~ spl0_40 ),
inference(superposition,[],[f1322,f1326]) ).
fof(f1617,plain,
( sk_c11 = inverse(identity)
| ~ spl0_40
| ~ spl0_41 ),
inference(superposition,[],[f1330,f1326]) ).
fof(f1618,plain,
( $false
| spl0_38
| ~ spl0_40
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f1617,f1318]) ).
fof(f1619,plain,
( spl0_38
| ~ spl0_40
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[],[f1618]) ).
fof(f1620,plain,
( $false
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| spl0_39
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1616,f1254]) ).
fof(f1621,plain,
( ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| spl0_39
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f1620]) ).
fof(f1629,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_38 ),
inference(forward_demodulation,[],[f1317,f1254]) ).
fof(f1633,plain,
( identity = multiply(sk_c2,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_27
| ~ spl0_39 ),
inference(forward_demodulation,[],[f1527,f1254]) ).
fof(f1643,plain,
( identity = sk_c9
| ~ spl0_9
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f909,f1326]) ).
fof(f1664,plain,
( spl0_26
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| ~ spl0_27
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f1633,f1320,f823,f222,f158,f149,f141,f819]) ).
fof(f1698,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_40 ),
inference(forward_demodulation,[],[f133,f1326]) ).
fof(f1699,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1698,f1643]) ).
fof(f1700,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1699,f1326]) ).
fof(f1702,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27
| ~ spl0_40 ),
inference(superposition,[],[f1700,f1]) ).
fof(f1706,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f1702]) ).
fof(f1710,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_26
| ~ spl0_27
| ~ spl0_38
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1706,f1629]) ).
fof(f1711,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_26
| ~ spl0_27
| ~ spl0_38
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f1710]) ).
fof(f1712,plain,
( ! [X6,X4] :
( identity != 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_7
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_demodulation,[],[f130,f1254]) ).
fof(f1713,plain,
( ! [X6,X4] :
( sk_c11 != multiply(inverse(X4),identity)
| identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1712,f1326]) ).
fof(f1714,plain,
( ! [X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| identity != multiply(X4,inverse(X4))
| identity != multiply(inverse(X4),identity)
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1713,f1254]) ).
fof(f1716,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| identity != multiply(identity,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_40 ),
inference(superposition,[],[f1714,f1251]) ).
fof(f1728,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c11,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1716,f1]) ).
fof(f1733,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1728,f1254]) ).
fof(f1738,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1733,f1]) ).
fof(f1782,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_40 ),
inference(superposition,[],[f1738,f3]) ).
fof(f1783,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_38
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1782,f1629]) ).
fof(f1785,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_38
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1783,f1629]) ).
fof(f1787,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_38
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1785,f1629]) ).
fof(f1790,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_38
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1787,f1629]) ).
fof(f1791,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_38
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f1790,f1629]) ).
fof(f1792,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_38
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f1791]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f152]) ).
cnf(s6,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f181]) ).
cnf(s7,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f186]) ).
cnf(s8,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f191]) ).
cnf(s9,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f196]) ).
cnf(s10,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f201]) ).
cnf(s11,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f206]) ).
cnf(s16,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f215]) ).
cnf(s17,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f216]) ).
cnf(s20,plain,
( spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f219]) ).
cnf(s21,plain,
( spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f220]) ).
cnf(s26,plain,
( spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f229]) ).
cnf(s27,plain,
( spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f230]) ).
cnf(s30,plain,
( spl0_17
| spl0_20 ),
inference(sat_conversion,[],[f233]) ).
cnf(s31,plain,
( spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f234]) ).
cnf(s36,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f239]) ).
cnf(s37,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f240]) ).
cnf(s38,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f241]) ).
cnf(s39,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f242]) ).
cnf(s40,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f243]) ).
cnf(s41,plain,
( spl0_5
| spl0_18 ),
inference(sat_conversion,[],[f244]) ).
cnf(s46,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f249]) ).
cnf(s47,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f250]) ).
cnf(s48,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f251]) ).
cnf(s49,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f252]) ).
cnf(s50,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f253]) ).
cnf(s51,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f254]) ).
cnf(s56,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f259]) ).
cnf(s57,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f260]) ).
cnf(s60,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f263]) ).
cnf(s61,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f264]) ).
cnf(s62,plain,
( spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f540]) ).
cnf(s63,plain,
( spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f547]) ).
cnf(s64,plain,
( spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f555]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f581]) ).
cnf(s75,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f639]) ).
cnf(s94,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_20
| spl0_27 ),
inference(sat_conversion,[],[f830]) ).
cnf(s110,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f975]) ).
cnf(s123,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| ~ spl0_26
| ~ spl0_27 ),
inference(sat_conversion,[],[f1095]) ).
cnf(s124,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| spl0_26 ),
inference(sat_conversion,[],[f1139]) ).
cnf(s130,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1194]) ).
cnf(s133,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1246]) ).
cnf(s135,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27 ),
inference(sat_conversion,[],[f1292]) ).
cnf(s138,plain,
( ~ spl0_20
| spl0_27
| ~ spl0_40 ),
inference(sat_conversion,[],[f1334]) ).
cnf(s146,plain,
( ~ spl0_7
| ~ spl0_39
| spl0_41 ),
inference(sat_conversion,[],[f1402]) ).
cnf(s156,plain,
( ~ spl0_19
| ~ spl0_20
| spl0_40 ),
inference(sat_conversion,[],[f1557]) ).
cnf(s161,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f1600]) ).
cnf(s164,plain,
( spl0_38
| ~ spl0_40
| ~ spl0_41 ),
inference(sat_conversion,[],[f1619]) ).
cnf(s165,plain,
( ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| spl0_39
| ~ spl0_40 ),
inference(sat_conversion,[],[f1621]) ).
cnf(s169,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_20
| spl0_26
| ~ spl0_27
| ~ spl0_39 ),
inference(sat_conversion,[],[f1664]) ).
cnf(s171,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_19
| ~ spl0_20
| ~ spl0_26
| ~ spl0_27
| ~ spl0_38
| ~ spl0_40 ),
inference(sat_conversion,[],[f1711]) ).
cnf(s175,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_27
| ~ spl0_38
| ~ spl0_40 ),
inference(sat_conversion,[],[f1792]) ).
cnf(s176,plain,
spl0_5,
inference(rat,[],[s63,s36,s37,s38,s39,s40,s41]) ).
cnf(s177,plain,
spl0_6,
inference(rat,[],[s64,s46,s47,s48,s49,s50,s51]) ).
cnf(s178,plain,
spl0_7,
inference(rat,[],[s62,s56,s57,s60,s61]) ).
cnf(s179,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s75,s8,s9,s10,s11]) ).
cnf(s180,plain,
( spl0_18
| ~ spl0_4 ),
inference(rat,[],[s161,s21,s31,s179]) ).
cnf(s181,plain,
~ spl0_4,
inference(rat,[],[s161,s20,s30,s130,s180,s179,s178,s177]) ).
cnf(s182,plain,
( spl0_18
| ~ spl0_3 ),
inference(rat,[],[s138,s156,s135,s21,s31,s178]) ).
cnf(s183,plain,
( spl0_20
| ~ spl0_17
| ~ spl0_3 ),
inference(rat,[],[s66,s26,s27,s182]) ).
cnf(s184,plain,
( ~ spl0_17
| ~ spl0_3 ),
inference(rat,[],[s94,s135,s183,s182,s178]) ).
cnf(s185,plain,
~ spl0_3,
inference(rat,[],[s138,s156,s135,s20,s30,s184,s178]) ).
cnf(s186,plain,
( spl0_20
| ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s110,s26,s27,s30,s176]) ).
cnf(s187,plain,
( ~ spl0_9
| ~ spl0_19
| ~ spl0_2
| ~ spl0_18
| ~ spl0_17
| ~ spl0_27 ),
inference(rat,[],[s124,s123,s178,s177]) ).
cnf(s188,plain,
( spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s110,s6,s7,s176]) ).
cnf(s189,plain,
( ~ spl0_9
| ~ spl0_27
| ~ spl0_2
| ~ spl0_18
| ~ spl0_17 ),
inference(rat,[],[s110,s16,s17,s187,s176]) ).
cnf(s190,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s189,s188,s94,s186]) ).
cnf(s191,plain,
( ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s164,s171,s146,s169,s165,s138,s156,s10,s20,s190,s186,s176,s178]) ).
cnf(s192,plain,
~ spl0_2,
inference(rat,[],[s164,s171,s146,s169,s165,s138,s156,s11,s21,s31,s191,s178,s176]) ).
cnf(s193,plain,
spl0_1,
inference(rat,[],[s1,s177,s176,s181,s178,s185,s192]) ).
cnf(s194,plain,
( ~ spl0_40
| ~ spl0_20
| ~ spl0_27 ),
inference(rat,[],[s146,s164,s165,s175,s193,s178]) ).
cnf(s195,plain,
( ~ spl0_40
| ~ spl0_20 ),
inference(rat,[],[s194,s138]) ).
cnf(s196,plain,
( ~ spl0_19
| ~ spl0_20 ),
inference(rat,[],[s195,s156]) ).
cnf(s197,plain,
spl0_17,
inference(rat,[],[s196,s20,s30]) ).
cnf(s198,plain,
~ spl0_18,
inference(rat,[],[s133,s193,s178,s197]) ).
cnf(s199,plain,
spl0_20,
inference(rat,[],[s31,s198]) ).
cnf(s200,plain,
spl0_19,
inference(rat,[],[s21,s198]) ).
cnf(s203,plain,
$false,
inference(rat,[],[s196,s199,s200]) ).
fof(f1793,plain,
$false,
inference(avatar_sat_refutation,[],[s203]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP384-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:00:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.47 % (3266820)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (3266828)dis+10_1_sil=32000:sp=arity:random_seed=2342310580:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (3266826)% WARNING: option uhcvi not known.
% 0.16/0.47 % (3266825)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2278868448_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (3266826)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2669806694:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (3266827)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2036598535:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (3266829)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=728438284:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (3266830)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=113246499:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (3266831)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1282772163:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (3266828) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3266820-3266828"...
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % (3266828)...printing done.
% 0.16/0.47 % (3266828)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3266828)------------------------------
% 0.16/0.47 % (3266828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3266828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3266828)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3266828)Termination reason: Refutation
% 0.16/0.47 % (3266828)Time elapsed: 0.019 s
% 0.16/0.47 % (3266828)Peak memory usage: 13 MB
% 0.16/0.47 % (3266828)Instructions burned: 56 (million)
% 0.16/0.47 % (3266820)Success in time 0.052 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------