%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL020-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:33:47 PM UTC 2026
% Result : Unsatisfiable 17.80s 3.36s
% Output : Refutation 18.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 56
% Syntax : Number of formulae : 488 ( 136 unt; 41 def)
% Number of atoms : 1417 ( 398 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 1830 ( 901 ~; 897 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 34 ( 32 usr; 33 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 14 con; 0-2 aty)
% Number of variables : 299 ( 0 sgn 299 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
fof(f17,negated_conjecture,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
sk1 = composition(sk1,top),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
composition(meet(sk1,one),sk2) != meet(sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f21,plain,
composition(complement(join(complement(sk1),complement(one))),sk2) != complement(join(complement(sk1),complement(sk2))),
inference(definition_unfolding,[],[f19,f6,f6]) ).
fof(f22,definition,
sF0 = composition(sk1,top),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f23,plain,
composition(sk1,top) = sF0,
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
sk1 = sF0,
inference(definition_folding,[],[f18,f23]) ).
fof(f25,definition,
sF1 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f26,plain,
complement(sk1) = sF1,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF2 = complement(one),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f28,plain,
complement(one) = sF2,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF3 = join(sF1,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f30,plain,
join(sF1,sF2) = sF3,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f32,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF5 = composition(sF4,sk2),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f34,plain,
composition(sF4,sk2) = sF5,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF6 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f36,plain,
complement(sk2) = sF6,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF7 = join(sF1,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f38,plain,
join(sF1,sF6) = sF7,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF8 = complement(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f40,plain,
complement(sF7) = sF8,
inference(reorient_equations,[],[f39]) ).
fof(f41,plain,
sF5 != sF8,
inference(definition_folding,[],[f21,f40,f38,f36,f26,f34,f32,f30,f28,f26]) ).
fof(f42,plain,
zero = complement(top),
inference(backward_demodulation,[],[f20,f15]) ).
fof(f43,plain,
sF0 = composition(sF0,top),
inference(forward_demodulation,[],[f23,f24]) ).
fof(f44,plain,
sF1 = complement(sF0),
inference(forward_demodulation,[],[f26,f24]) ).
fof(f45,plain,
sF3 = join(sF2,sF1),
inference(forward_demodulation,[],[f30,f1]) ).
fof(f46,plain,
sF7 = join(sF6,sF1),
inference(forward_demodulation,[],[f38,f1]) ).
fof(f48,definition,
( spl9_1
<=> sF0 = composition(sF0,top) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f50,plain,
( sF0 = composition(sF0,top)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
spl9_1,
inference(avatar_split_clause,[],[f43,f48]) ).
fof(f58,definition,
( spl9_3
<=> complement(sF7) = sF8 ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f60,plain,
( complement(sF7) = sF8
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
spl9_3,
inference(avatar_split_clause,[],[f40,f58]) ).
fof(f63,definition,
( spl9_4
<=> composition(sF4,sk2) = sF5 ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f65,plain,
( composition(sF4,sk2) = sF5
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,plain,
spl9_4,
inference(avatar_split_clause,[],[f34,f63]) ).
fof(f68,definition,
( spl9_5
<=> sF5 = sF8 ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f70,plain,
( sF5 != sF8
| spl9_5 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
~ spl9_5,
inference(avatar_split_clause,[],[f41,f68]) ).
fof(f74,plain,
( ! [X0] : composition(join(X0,sF0),top) = join(composition(X0,top),sF0)
| ~ spl9_1 ),
inference(superposition,[],[f9,f50]) ).
fof(f85,plain,
( ! [X0] : join(sF0,composition(X0,top)) = composition(join(X0,sF0),top)
| ~ spl9_1 ),
inference(forward_demodulation,[],[f74,f1]) ).
fof(f87,definition,
( spl9_6
<=> complement(sk2) = sF6 ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
fof(f89,plain,
( complement(sk2) = sF6
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
spl9_6,
inference(avatar_split_clause,[],[f36,f87]) ).
fof(f91,plain,
! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)),
inference(superposition,[],[f14,f10]) ).
fof(f92,plain,
( complement(top) = join(composition(converse(sF0),complement(sF0)),complement(top))
| ~ spl9_1 ),
inference(superposition,[],[f14,f50]) ).
fof(f103,plain,
( complement(top) = join(complement(top),composition(converse(sF0),complement(sF0)))
| ~ spl9_1 ),
inference(forward_demodulation,[],[f92,f1]) ).
fof(f104,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(forward_demodulation,[],[f91,f1]) ).
fof(f106,plain,
( complement(top) = join(complement(top),composition(converse(sF0),sF1))
| ~ spl9_1 ),
inference(forward_demodulation,[],[f103,f44]) ).
fof(f107,plain,
( zero = join(zero,composition(converse(sF0),sF1))
| ~ spl9_1 ),
inference(forward_demodulation,[],[f106,f42]) ).
fof(f109,definition,
( spl9_7
<=> sF1 = complement(sF0) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
fof(f111,plain,
( sF1 = complement(sF0)
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
spl9_7,
inference(avatar_split_clause,[],[f44,f109]) ).
fof(f117,plain,
( top = join(sF0,sF1)
| ~ spl9_7 ),
inference(superposition,[],[f15,f111]) ).
fof(f118,plain,
( top = join(sF1,sF0)
| ~ spl9_7 ),
inference(forward_demodulation,[],[f117,f1]) ).
fof(f121,definition,
( spl9_8
<=> complement(sF3) = sF4 ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
fof(f123,plain,
( complement(sF3) = sF4
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
spl9_8,
inference(avatar_split_clause,[],[f32,f121]) ).
fof(f135,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f4,f1]) ).
fof(f143,plain,
! [X0] : join(complement(join(complement(X0),complement(complement(complement(X0))))),complement(top)) = X0,
inference(superposition,[],[f4,f15]) ).
fof(f148,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f143,f1]) ).
fof(f156,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(forward_demodulation,[],[f135,f1]) ).
fof(f164,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f148,f42]) ).
fof(f172,definition,
( spl9_9
<=> sF7 = join(sF6,sF1) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
fof(f174,plain,
( sF7 = join(sF6,sF1)
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,plain,
spl9_9,
inference(avatar_split_clause,[],[f46,f172]) ).
fof(f177,definition,
( spl9_10
<=> complement(one) = sF2 ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
fof(f179,plain,
( complement(one) = sF2
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f180,plain,
spl9_10,
inference(avatar_split_clause,[],[f28,f177]) ).
fof(f191,definition,
( spl9_11
<=> sF3 = join(sF2,sF1) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
fof(f193,plain,
( sF3 = join(sF2,sF1)
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
spl9_11,
inference(avatar_split_clause,[],[f45,f191]) ).
fof(f196,definition,
( spl9_12
<=> zero = complement(top) ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
fof(f198,plain,
( zero = complement(top)
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f199,plain,
spl9_12,
inference(avatar_split_clause,[],[f42,f196]) ).
fof(f209,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f211,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f2,f4]) ).
fof(f214,plain,
( ! [X0] : join(sF2,join(sF1,X0)) = join(sF3,X0)
| ~ spl9_11 ),
inference(superposition,[],[f2,f193]) ).
fof(f220,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f221,plain,
! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))),
inference(superposition,[],[f15,f2]) ).
fof(f223,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(X2,complement(join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f211,f220]) ).
fof(f228,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f11,f10]) ).
fof(f256,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f156,f15]) ).
fof(f264,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f256,f1]) ).
fof(f280,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f264,f1]) ).
fof(f285,plain,
( ! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0)))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f280,f198]) ).
fof(f289,plain,
( ! [X0] : complement(complement(X0)) = X0
| ~ spl9_12 ),
inference(backward_demodulation,[],[f164,f285]) ).
fof(f292,plain,
( ! [X0] : complement(X0) = join(zero,complement(join(X0,X0)))
| ~ spl9_12 ),
inference(backward_demodulation,[],[f285,f289]) ).
fof(f298,plain,
( one = complement(sF2)
| ~ spl9_10
| ~ spl9_12 ),
inference(superposition,[],[f289,f179]) ).
fof(f299,plain,
( sk2 = complement(sF6)
| ~ spl9_6
| ~ spl9_12 ),
inference(superposition,[],[f289,f89]) ).
fof(f300,plain,
( sF0 = complement(sF1)
| ~ spl9_7
| ~ spl9_12 ),
inference(superposition,[],[f289,f111]) ).
fof(f301,plain,
( sF3 = complement(sF4)
| ~ spl9_8
| ~ spl9_12 ),
inference(superposition,[],[f289,f123]) ).
fof(f303,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,complement(X1))),complement(join(X0,X1)))
| ~ spl9_12 ),
inference(superposition,[],[f4,f289]) ).
fof(f308,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0)))
| ~ spl9_12 ),
inference(superposition,[],[f156,f289]) ).
fof(f314,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f303,f1]) ).
fof(f322,plain,
( ! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0))))
| ~ spl9_12 ),
inference(superposition,[],[f314,f1]) ).
fof(f345,plain,
( ! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),join(X0,complement(X1)))))
| ~ spl9_12 ),
inference(superposition,[],[f4,f314]) ).
fof(f349,plain,
( ! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(join(X0,complement(X1)),complement(join(X0,X1)))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f345,f1]) ).
fof(f368,plain,
( ! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(X0,join(complement(X1),complement(join(X0,X1))))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f349,f2]) ).
fof(f380,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1))))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f368,f289]) ).
fof(f397,plain,
( ! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(complement(X0),X1)))
| ~ spl9_12 ),
inference(superposition,[],[f308,f1]) ).
fof(f517,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f521,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f9,f12]) ).
fof(f529,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f521,f12]) ).
fof(f541,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f529,f11]) ).
fof(f544,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f541,f11]) ).
fof(f546,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f544,f12]) ).
fof(f559,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f546]) ).
fof(f572,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f559,f10]) ).
fof(f592,plain,
! [X0,X1] : composition(X0,join(one,X1)) = join(X0,composition(X0,X1)),
inference(superposition,[],[f572,f8]) ).
fof(f595,plain,
( ! [X0] : composition(sF4,join(sk2,X0)) = join(sF5,composition(sF4,X0))
| ~ spl9_4 ),
inference(superposition,[],[f572,f65]) ).
fof(f596,plain,
! [X0,X1] : composition(X0,join(X1,one)) = join(composition(X0,X1),X0),
inference(superposition,[],[f572,f8]) ).
fof(f606,plain,
! [X2,X3,X0,X1] : join(composition(X0,join(X1,X2)),X3) = join(composition(X0,X1),join(composition(X0,X2),X3)),
inference(superposition,[],[f2,f572]) ).
fof(f615,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(X1,one)),
inference(forward_demodulation,[],[f596,f1]) ).
fof(f642,plain,
! [X0,X1] : join(X0,join(complement(X0),complement(X1))) = join(complement(join(complement(X0),X1)),top),
inference(superposition,[],[f223,f15]) ).
fof(f647,plain,
( ! [X0,X1] : join(X1,complement(join(complement(X0),X1))) = join(complement(join(complement(X1),X0)),complement(complement(X0)))
| ~ spl9_12 ),
inference(superposition,[],[f223,f308]) ).
fof(f662,plain,
( ! [X0,X1] : join(X1,complement(join(complement(X0),X1))) = join(complement(complement(X0)),complement(join(complement(X1),X0)))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f647,f1]) ).
fof(f666,plain,
! [X0,X1] : join(X0,join(complement(X0),complement(X1))) = join(top,complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f642,f1]) ).
fof(f693,plain,
( ! [X0,X1] : join(X1,complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X1),X0)))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f662,f289]) ).
fof(f694,plain,
! [X0,X1] : join(top,complement(join(complement(X0),X1))) = join(top,complement(X1)),
inference(forward_demodulation,[],[f666,f209]) ).
fof(f752,definition,
( spl9_13
<=> sk2 = complement(sF6) ),
introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition]) ).
fof(f754,plain,
( sk2 = complement(sF6)
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f752]) ).
fof(f755,plain,
( spl9_13
| ~ spl9_6
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f299,f196,f87,f752]) ).
fof(f770,plain,
( complement(sF1) = join(complement(sF3),complement(join(sF1,complement(sF2))))
| ~ spl9_11
| ~ spl9_12 ),
inference(superposition,[],[f322,f193]) ).
fof(f788,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(join(complement(join(X0,complement(X1))),join(X1,X0))),complement(complement(X0)))
| ~ spl9_12 ),
inference(superposition,[],[f308,f322]) ).
fof(f798,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(complement(join(X0,complement(X1))),join(X1,X0))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f788,f1]) ).
fof(f809,plain,
( complement(sF1) = join(complement(sF3),complement(join(sF1,one)))
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f770,f298]) ).
fof(f821,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(join(X1,X0),complement(join(X0,complement(X1))))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f798,f1]) ).
fof(f830,plain,
( complement(sF1) = join(sF4,complement(join(sF1,one)))
| ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f809,f123]) ).
fof(f840,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,complement(join(X0,complement(X1)))))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f821,f2]) ).
fof(f847,plain,
( sF0 = join(sF4,complement(join(sF1,one)))
| ~ spl9_7
| ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f830,f300]) ).
fof(f856,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1)))))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f840,f289]) ).
fof(f868,plain,
( ! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1)))))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f856,f289]) ).
fof(f874,definition,
( spl9_14
<=> sF0 = complement(sF1) ),
introduced(definition,[new_symbols(definition,[spl9_14])],[avatar_definition]) ).
fof(f876,plain,
( sF0 = complement(sF1)
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f874]) ).
fof(f877,plain,
( spl9_14
| ~ spl9_7
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f300,f196,f109,f874]) ).
fof(f883,plain,
( top = complement(zero)
| ~ spl9_12 ),
inference(superposition,[],[f289,f198]) ).
fof(f885,plain,
( ! [X0] : complement(X0) = join(complement(join(X0,top)),complement(join(X0,zero)))
| ~ spl9_12 ),
inference(superposition,[],[f314,f198]) ).
fof(f887,plain,
( ! [X0] : complement(X0) = join(complement(join(X0,zero)),complement(join(X0,top)))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f885,f1]) ).
fof(f896,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f517,f8]) ).
fof(f914,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f896,f10]) ).
fof(f931,plain,
! [X0] : complement(X0) = join(complement(X0),composition(one,complement(X0))),
inference(superposition,[],[f104,f914]) ).
fof(f935,plain,
! [X0,X1] : composition(join(converse(one),X1),X0) = join(X0,composition(X1,X0)),
inference(superposition,[],[f9,f914]) ).
fof(f941,plain,
one = converse(one),
inference(superposition,[],[f8,f914]) ).
fof(f944,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f914,f941]) ).
fof(f951,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(forward_demodulation,[],[f935,f941]) ).
fof(f956,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f931,f944]) ).
fof(f977,plain,
( ! [X0] : join(X0,X0) = X0
| ~ spl9_12 ),
inference(superposition,[],[f956,f289]) ).
fof(f991,plain,
( ! [X0] : complement(complement(X0)) = join(complement(complement(X0)),complement(join(complement(X0),complement(complement(X0)))))
| ~ spl9_12 ),
inference(superposition,[],[f314,f956]) ).
fof(f993,plain,
( ! [X0] : complement(complement(X0)) = join(X0,complement(join(complement(complement(complement(X0))),X0)))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f991,f693]) ).
fof(f1003,plain,
( ! [X0] : complement(X0) = join(zero,complement(X0))
| ~ spl9_12 ),
inference(backward_demodulation,[],[f292,f977]) ).
fof(f1004,plain,
( ! [X0] : complement(complement(X0)) = join(X0,complement(join(X0,complement(complement(complement(X0))))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f993,f1]) ).
fof(f1013,plain,
( ! [X0] : complement(complement(X0)) = join(X0,complement(join(X0,complement(X0))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1004,f289]) ).
fof(f1022,plain,
( ! [X0] : complement(complement(X0)) = join(X0,complement(top))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1013,f15]) ).
fof(f1030,plain,
( ! [X0] : complement(complement(X0)) = join(X0,zero)
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1022,f198]) ).
fof(f1037,plain,
( ! [X0] : join(X0,zero) = X0
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1030,f289]) ).
fof(f1041,plain,
( ! [X0] : complement(X0) = join(complement(X0),complement(join(X0,top)))
| ~ spl9_12 ),
inference(backward_demodulation,[],[f887,f1037]) ).
fof(f1066,plain,
( ! [X0] : join(zero,X0) = X0
| ~ spl9_12 ),
inference(superposition,[],[f1003,f289]) ).
fof(f1087,plain,
( zero = composition(converse(sF0),sF1)
| ~ spl9_1
| ~ spl9_12 ),
inference(backward_demodulation,[],[f107,f1066]) ).
fof(f1165,plain,
( ! [X0] : complement(complement(join(X0,top))) = join(complement(complement(X0)),complement(join(complement(join(X0,top)),complement(complement(X0)))))
| ~ spl9_12 ),
inference(superposition,[],[f322,f1041]) ).
fof(f1171,plain,
( ! [X0] : complement(complement(join(X0,top))) = join(join(X0,top),complement(join(complement(complement(complement(X0))),join(X0,top))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1165,f693]) ).
fof(f1183,plain,
( ! [X0] : complement(complement(join(X0,top))) = join(X0,join(top,complement(join(complement(complement(complement(X0))),join(X0,top)))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1171,f2]) ).
fof(f1192,plain,
( ! [X0] : complement(complement(join(X0,top))) = join(X0,join(top,complement(join(X0,top))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1183,f694]) ).
fof(f1198,plain,
( ! [X0] : top = complement(complement(join(X0,top)))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1192,f221]) ).
fof(f1202,plain,
( ! [X0] : top = join(X0,top)
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1198,f289]) ).
fof(f1233,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1))
| ~ spl9_12 ),
inference(superposition,[],[f2,f977]) ).
fof(f1273,definition,
( spl9_16
<=> zero = composition(converse(sF0),sF1) ),
introduced(definition,[new_symbols(definition,[spl9_16])],[avatar_definition]) ).
fof(f1275,plain,
( zero = composition(converse(sF0),sF1)
| ~ spl9_16 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f1276,plain,
( spl9_16
| ~ spl9_1
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f1087,f196,f48,f1273]) ).
fof(f1286,plain,
( ! [X0,X1] : join(join(X0,X1),complement(X0)) = join(top,complement(join(X0,complement(X1))))
| ~ spl9_12 ),
inference(superposition,[],[f209,f314]) ).
fof(f1289,plain,
( ! [X0] : join(X0,complement(X0)) = join(top,complement(X0))
| ~ spl9_12 ),
inference(superposition,[],[f209,f977]) ).
fof(f1291,plain,
! [X0,X1] : join(top,X0) = join(X1,join(X0,complement(X1))),
inference(superposition,[],[f209,f1]) ).
fof(f1314,plain,
( ! [X0] : top = join(top,complement(X0))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1289,f15]) ).
fof(f1317,plain,
( ! [X0,X1] : join(X0,join(X1,complement(X0))) = join(top,complement(join(X0,complement(X1))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1286,f2]) ).
fof(f1333,plain,
( ! [X0,X1] : top = join(X0,join(X1,complement(X0)))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1317,f1314]) ).
fof(f1340,plain,
( ! [X1] : top = join(top,X1)
| ~ spl9_12 ),
inference(forward_demodulation,[],[f1333,f1291]) ).
fof(f1385,plain,
( composition(converse(sF1),sF0) = converse(zero)
| ~ spl9_16 ),
inference(superposition,[],[f517,f1275]) ).
fof(f1414,plain,
( join(sF5,composition(sF4,complement(sk2))) = composition(sF4,top)
| ~ spl9_4 ),
inference(superposition,[],[f595,f15]) ).
fof(f1429,plain,
( composition(sF4,top) = join(sF5,composition(sF4,sF6))
| ~ spl9_4
| ~ spl9_6 ),
inference(forward_demodulation,[],[f1414,f89]) ).
fof(f1517,plain,
! [X0] : composition(X0,top) = join(X0,composition(X0,complement(one))),
inference(superposition,[],[f592,f15]) ).
fof(f1572,plain,
( ! [X0] : composition(X0,top) = join(X0,composition(X0,sF2))
| ~ spl9_10 ),
inference(forward_demodulation,[],[f1517,f179]) ).
fof(f1606,plain,
( ! [X0] : composition(X0,top) = join(X0,composition(X0,top))
| ~ spl9_12 ),
inference(superposition,[],[f592,f1202]) ).
fof(f1636,plain,
! [X0] : converse(top) = join(X0,converse(complement(converse(X0)))),
inference(superposition,[],[f228,f15]) ).
fof(f1883,plain,
( top = converse(top)
| ~ spl9_12 ),
inference(superposition,[],[f1340,f1636]) ).
fof(f1892,plain,
( ! [X0] : top = join(X0,converse(complement(converse(X0))))
| ~ spl9_12 ),
inference(backward_demodulation,[],[f1636,f1883]) ).
fof(f2011,definition,
( spl9_17
<=> top = converse(top) ),
introduced(definition,[new_symbols(definition,[spl9_17])],[avatar_definition]) ).
fof(f2013,plain,
( top = converse(top)
| ~ spl9_17 ),
inference(avatar_component_clause,[],[f2011]) ).
fof(f2014,plain,
( spl9_17
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f1883,f196,f2011]) ).
fof(f2123,plain,
( ! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0))
| ~ spl9_12 ),
inference(superposition,[],[f220,f977]) ).
fof(f2374,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(X0))
| ~ spl9_12 ),
inference(superposition,[],[f1233,f314]) ).
fof(f2375,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0))
| ~ spl9_12 ),
inference(superposition,[],[f1233,f322]) ).
fof(f2436,plain,
( ! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0)))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2375,f1]) ).
fof(f2437,plain,
( ! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1)))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2374,f1]) ).
fof(f2453,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1))))
| ~ spl9_12 ),
inference(backward_demodulation,[],[f380,f2436]) ).
fof(f2461,plain,
( ! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1))))
| ~ spl9_12 ),
inference(backward_demodulation,[],[f868,f2453]) ).
fof(f2469,plain,
( ! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1)))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2461,f2123]) ).
fof(f2522,plain,
( complement(sF2) = join(complement(sF2),complement(sF3))
| ~ spl9_11
| ~ spl9_12 ),
inference(superposition,[],[f2437,f193]) ).
fof(f2553,plain,
( complement(sF2) = join(complement(sF2),sF4)
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2522,f123]) ).
fof(f2571,plain,
( complement(sF2) = join(sF4,complement(sF2))
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2553,f1]) ).
fof(f2584,plain,
( one = join(sF4,one)
| ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2571,f298]) ).
fof(f2607,plain,
( ! [X0,X1] : join(X1,complement(X0)) = join(X1,complement(join(X0,X1)))
| ~ spl9_12 ),
inference(superposition,[],[f2469,f1]) ).
fof(f2613,plain,
( ! [X0] : join(X0,complement(composition(X0,sF2))) = join(X0,complement(composition(X0,top)))
| ~ spl9_10
| ~ spl9_12 ),
inference(superposition,[],[f2469,f1572]) ).
fof(f2614,plain,
( ! [X0] : join(X0,complement(top)) = join(X0,complement(converse(complement(converse(X0)))))
| ~ spl9_12 ),
inference(superposition,[],[f2469,f1892]) ).
fof(f2629,plain,
( join(sF2,complement(sF1)) = join(sF2,complement(sF3))
| ~ spl9_11
| ~ spl9_12 ),
inference(superposition,[],[f2469,f193]) ).
fof(f2686,plain,
( join(sF2,complement(sF1)) = join(sF2,sF4)
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2629,f123]) ).
fof(f2697,plain,
( ! [X0] : join(X0,zero) = join(X0,complement(converse(complement(converse(X0)))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2614,f198]) ).
fof(f2719,plain,
( join(sF2,sF0) = join(sF2,sF4)
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14 ),
inference(forward_demodulation,[],[f2686,f876]) ).
fof(f2729,plain,
( ! [X0] : join(X0,complement(converse(complement(converse(X0))))) = X0
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2697,f1037]) ).
fof(f2819,plain,
( join(sF1,complement(sF2)) = join(sF1,complement(sF3))
| ~ spl9_11
| ~ spl9_12 ),
inference(superposition,[],[f2607,f193]) ).
fof(f2879,plain,
( join(sF1,complement(sF2)) = join(sF1,sF4)
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2819,f123]) ).
fof(f2914,plain,
( join(sF1,complement(sF2)) = join(sF4,sF1)
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2879,f1]) ).
fof(f2938,plain,
( join(sF1,one) = join(sF4,sF1)
| ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2914,f298]) ).
fof(f2955,plain,
( sF0 = join(sF4,complement(join(sF4,sF1)))
| ~ spl9_7
| ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12 ),
inference(backward_demodulation,[],[f847,f2938]) ).
fof(f2967,plain,
( sF0 = join(sF4,complement(sF1))
| ~ spl9_7
| ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12 ),
inference(forward_demodulation,[],[f2955,f2469]) ).
fof(f2976,plain,
( sF0 = join(sF4,sF0)
| ~ spl9_7
| ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14 ),
inference(forward_demodulation,[],[f2967,f876]) ).
fof(f2996,definition,
( spl9_18
<=> one = join(sF4,one) ),
introduced(definition,[new_symbols(definition,[spl9_18])],[avatar_definition]) ).
fof(f2998,plain,
( one = join(sF4,one)
| ~ spl9_18 ),
inference(avatar_component_clause,[],[f2996]) ).
fof(f2999,plain,
( spl9_18
| ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f2584,f196,f191,f177,f121,f2996]) ).
fof(f3186,definition,
( spl9_20
<=> join(sF1,one) = join(sF4,sF1) ),
introduced(definition,[new_symbols(definition,[spl9_20])],[avatar_definition]) ).
fof(f3188,plain,
( join(sF1,one) = join(sF4,sF1)
| ~ spl9_20 ),
inference(avatar_component_clause,[],[f3186]) ).
fof(f3189,plain,
( spl9_20
| ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f2938,f196,f191,f177,f121,f3186]) ).
fof(f3516,definition,
( spl9_21
<=> sF3 = complement(sF4) ),
introduced(definition,[new_symbols(definition,[spl9_21])],[avatar_definition]) ).
fof(f3518,plain,
( sF3 = complement(sF4)
| ~ spl9_21 ),
inference(avatar_component_clause,[],[f3516]) ).
fof(f3519,plain,
( spl9_21
| ~ spl9_8
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f301,f196,f121,f3516]) ).
fof(f3542,plain,
( ! [X0] : composition(X0,one) = join(X0,composition(X0,sF4))
| ~ spl9_18 ),
inference(superposition,[],[f615,f2998]) ).
fof(f3608,plain,
( ! [X0] : join(X0,composition(X0,sF4)) = X0
| ~ spl9_18 ),
inference(forward_demodulation,[],[f3542,f8]) ).
fof(f3653,definition,
( spl9_22
<=> one = complement(sF2) ),
introduced(definition,[new_symbols(definition,[spl9_22])],[avatar_definition]) ).
fof(f3655,plain,
( one = complement(sF2)
| ~ spl9_22 ),
inference(avatar_component_clause,[],[f3653]) ).
fof(f3656,plain,
( spl9_22
| ~ spl9_10
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f298,f196,f177,f3653]) ).
fof(f3684,plain,
( ! [X0] : composition(one,X0) = join(X0,composition(composition(one,sF4),X0))
| ~ spl9_18 ),
inference(superposition,[],[f951,f3608]) ).
fof(f3698,plain,
( ! [X0] : composition(one,X0) = join(X0,composition(one,composition(sF4,X0)))
| ~ spl9_18 ),
inference(forward_demodulation,[],[f3684,f7]) ).
fof(f3720,plain,
( ! [X0] : composition(one,X0) = join(X0,composition(sF4,X0))
| ~ spl9_18 ),
inference(forward_demodulation,[],[f3698,f944]) ).
fof(f3727,plain,
( ! [X0] : join(X0,composition(sF4,X0)) = X0
| ~ spl9_18 ),
inference(forward_demodulation,[],[f3720,f944]) ).
fof(f3824,definition,
( spl9_23
<=> top = join(sF1,sF0) ),
introduced(definition,[new_symbols(definition,[spl9_23])],[avatar_definition]) ).
fof(f3826,plain,
( top = join(sF1,sF0)
| ~ spl9_23 ),
inference(avatar_component_clause,[],[f3824]) ).
fof(f3827,plain,
( spl9_23
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f118,f109,f3824]) ).
fof(f4447,definition,
( spl9_25
<=> top = complement(zero) ),
introduced(definition,[new_symbols(definition,[spl9_25])],[avatar_definition]) ).
fof(f4449,plain,
( top = complement(zero)
| ~ spl9_25 ),
inference(avatar_component_clause,[],[f4447]) ).
fof(f4450,plain,
( spl9_25
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f883,f196,f4447]) ).
fof(f4987,definition,
( spl9_27
<=> composition(converse(sF1),sF0) = converse(zero) ),
introduced(definition,[new_symbols(definition,[spl9_27])],[avatar_definition]) ).
fof(f4989,plain,
( composition(converse(sF1),sF0) = converse(zero)
| ~ spl9_27 ),
inference(avatar_component_clause,[],[f4987]) ).
fof(f4990,plain,
( spl9_27
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f1385,f1273,f4987]) ).
fof(f4992,plain,
( complement(sF0) = join(complement(sF0),composition(sF1,complement(converse(zero))))
| ~ spl9_27 ),
inference(superposition,[],[f104,f4989]) ).
fof(f5012,plain,
( sF1 = join(sF1,composition(sF1,complement(converse(zero))))
| ~ spl9_7
| ~ spl9_27 ),
inference(forward_demodulation,[],[f4992,f111]) ).
fof(f5502,plain,
! [X2,X3,X0,X1] : join(composition(X0,join(X3,X2)),composition(X1,X2)) = join(composition(X0,X3),composition(join(X0,X1),X2)),
inference(superposition,[],[f606,f9]) ).
fof(f5797,plain,
( ! [X0,X1] : join(X1,X0) = join(X0,join(composition(sF4,X0),X1))
| ~ spl9_18 ),
inference(superposition,[],[f220,f3727]) ).
fof(f5810,plain,
( ! [X0] : complement(composition(sF4,complement(X0))) = join(complement(join(X0,composition(sF4,complement(X0)))),complement(complement(X0)))
| ~ spl9_12
| ~ spl9_18 ),
inference(superposition,[],[f397,f3727]) ).
fof(f5841,plain,
( ! [X0] : complement(composition(sF4,complement(X0))) = join(complement(complement(X0)),complement(join(X0,composition(sF4,complement(X0)))))
| ~ spl9_12
| ~ spl9_18 ),
inference(forward_demodulation,[],[f5810,f1]) ).
fof(f5866,plain,
( ! [X0] : complement(composition(sF4,complement(X0))) = join(X0,complement(join(X0,composition(sF4,complement(X0)))))
| ~ spl9_12
| ~ spl9_18 ),
inference(forward_demodulation,[],[f5841,f289]) ).
fof(f5875,plain,
( ! [X0] : complement(composition(sF4,complement(X0))) = join(X0,complement(composition(sF4,complement(X0))))
| ~ spl9_12
| ~ spl9_18 ),
inference(forward_demodulation,[],[f5866,f2469]) ).
fof(f5918,plain,
( ! [X0] : complement(complement(converse(complement(converse(complement(X0)))))) = join(complement(join(X0,complement(converse(complement(converse(complement(X0))))))),complement(complement(X0)))
| ~ spl9_12 ),
inference(superposition,[],[f397,f2729]) ).
fof(f5926,plain,
( ! [X0] : converse(converse(X0)) = join(X0,converse(complement(converse(complement(converse(converse(X0)))))))
| ~ spl9_12 ),
inference(superposition,[],[f228,f2729]) ).
fof(f5941,plain,
( ! [X0] : join(X0,converse(complement(converse(complement(X0))))) = X0
| ~ spl9_12 ),
inference(forward_demodulation,[],[f5926,f10]) ).
fof(f5948,plain,
( ! [X0] : complement(complement(converse(complement(converse(complement(X0)))))) = join(complement(complement(X0)),complement(join(X0,complement(converse(complement(converse(complement(X0))))))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f5918,f1]) ).
fof(f5971,plain,
( ! [X0] : complement(complement(converse(complement(converse(complement(X0)))))) = join(X0,complement(join(X0,complement(converse(complement(converse(complement(X0))))))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f5948,f289]) ).
fof(f5981,plain,
( ! [X0] : complement(complement(converse(complement(converse(complement(X0)))))) = join(X0,complement(complement(converse(complement(converse(complement(X0)))))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f5971,f2469]) ).
fof(f5983,plain,
( ! [X0] : converse(complement(converse(complement(X0)))) = join(X0,converse(complement(converse(complement(X0)))))
| ~ spl9_12 ),
inference(forward_demodulation,[],[f5981,f289]) ).
fof(f5985,plain,
( ! [X0] : converse(complement(converse(complement(X0)))) = X0
| ~ spl9_12 ),
inference(forward_demodulation,[],[f5983,f5941]) ).
fof(f5990,plain,
( zero = converse(complement(converse(top)))
| ~ spl9_12
| ~ spl9_25 ),
inference(superposition,[],[f5985,f4449]) ).
fof(f6051,plain,
( zero = converse(complement(top))
| ~ spl9_12
| ~ spl9_17
| ~ spl9_25 ),
inference(forward_demodulation,[],[f5990,f2013]) ).
fof(f6084,plain,
( zero = converse(zero)
| ~ spl9_12
| ~ spl9_17
| ~ spl9_25 ),
inference(forward_demodulation,[],[f6051,f198]) ).
fof(f6107,plain,
( sF1 = join(sF1,composition(sF1,complement(zero)))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_17
| ~ spl9_25
| ~ spl9_27 ),
inference(backward_demodulation,[],[f5012,f6084]) ).
fof(f6126,plain,
( sF1 = join(sF1,composition(sF1,top))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_17
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f6107,f4449]) ).
fof(f6131,plain,
( sF1 = composition(sF1,top)
| ~ spl9_7
| ~ spl9_12
| ~ spl9_17
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f6126,f1606]) ).
fof(f6460,definition,
( spl9_34
<=> join(sF2,sF0) = join(sF2,sF4) ),
introduced(definition,[new_symbols(definition,[spl9_34])],[avatar_definition]) ).
fof(f6462,plain,
( join(sF2,sF0) = join(sF2,sF4)
| ~ spl9_34 ),
inference(avatar_component_clause,[],[f6460]) ).
fof(f6463,plain,
( spl9_34
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14 ),
inference(avatar_split_clause,[],[f2719,f874,f196,f191,f121,f6460]) ).
fof(f7135,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(join(X0,X2),complement(X1))) = join(composition(X0,top),composition(X2,complement(X1))),
inference(superposition,[],[f5502,f15]) ).
fof(f7290,plain,
( ! [X0,X1] : join(composition(sF4,join(X0,X1)),composition(one,X1)) = join(composition(sF4,X0),composition(one,X1))
| ~ spl9_18 ),
inference(superposition,[],[f5502,f2998]) ).
fof(f7373,plain,
( ! [X0,X1] : join(composition(sF4,X0),X1) = join(composition(sF4,join(X0,X1)),X1)
| ~ spl9_18 ),
inference(forward_demodulation,[],[f7290,f944]) ).
fof(f7479,plain,
( ! [X0,X1] : join(composition(sF4,X0),X1) = join(X1,composition(sF4,join(X0,X1)))
| ~ spl9_18 ),
inference(forward_demodulation,[],[f7373,f1]) ).
fof(f7610,plain,
( ! [X0,X1] : join(composition(sF4,X1),X0) = join(X0,composition(sF4,join(X0,X1)))
| ~ spl9_18 ),
inference(superposition,[],[f7479,f1]) ).
fof(f7616,plain,
( ! [X0] : join(composition(sF4,X0),complement(X0)) = join(complement(X0),composition(sF4,top))
| ~ spl9_18 ),
inference(superposition,[],[f7479,f15]) ).
fof(f7654,plain,
( join(composition(sF4,sF1),sF0) = join(sF0,composition(sF4,top))
| ~ spl9_18
| ~ spl9_23 ),
inference(superposition,[],[f7479,f3826]) ).
fof(f7658,plain,
( join(composition(sF4,sF2),sF0) = join(sF0,composition(sF4,join(sF2,sF4)))
| ~ spl9_18
| ~ spl9_34 ),
inference(superposition,[],[f7479,f6462]) ).
fof(f7659,plain,
( join(composition(sF4,sF2),sF1) = join(sF1,composition(sF4,sF3))
| ~ spl9_11
| ~ spl9_18 ),
inference(superposition,[],[f7479,f193]) ).
fof(f7747,plain,
( join(sF1,composition(sF4,sF3)) = join(sF1,composition(sF4,sF2))
| ~ spl9_11
| ~ spl9_18 ),
inference(forward_demodulation,[],[f7659,f1]) ).
fof(f7748,plain,
( join(sF0,composition(sF4,join(sF2,sF4))) = join(sF0,composition(sF4,sF2))
| ~ spl9_18
| ~ spl9_34 ),
inference(forward_demodulation,[],[f7658,f1]) ).
fof(f7751,plain,
( join(sF0,composition(sF4,sF1)) = join(sF0,composition(sF4,top))
| ~ spl9_18
| ~ spl9_23 ),
inference(forward_demodulation,[],[f7654,f1]) ).
fof(f7771,plain,
( ! [X0] : join(complement(X0),composition(sF4,X0)) = join(complement(X0),composition(sF4,top))
| ~ spl9_18 ),
inference(forward_demodulation,[],[f7616,f1]) ).
fof(f7858,plain,
( ! [X0] : join(composition(sF4,complement(X0)),X0) = join(X0,composition(sF4,top))
| ~ spl9_18 ),
inference(superposition,[],[f7610,f15]) ).
fof(f8034,plain,
( ! [X0] : join(X0,composition(sF4,complement(X0))) = join(X0,composition(sF4,top))
| ~ spl9_18 ),
inference(forward_demodulation,[],[f7858,f1]) ).
fof(f8128,plain,
( join(sF4,composition(sF4,top)) = join(sF4,composition(sF4,sF3))
| ~ spl9_18
| ~ spl9_21 ),
inference(superposition,[],[f8034,f3518]) ).
fof(f8190,plain,
( ! [X0] : join(X0,complement(join(X0,composition(sF4,complement(X0))))) = join(X0,complement(composition(sF4,top)))
| ~ spl9_12
| ~ spl9_18 ),
inference(superposition,[],[f2469,f8034]) ).
fof(f8199,plain,
( ! [X0] : join(X0,complement(composition(sF4,complement(X0)))) = join(X0,complement(composition(sF4,top)))
| ~ spl9_12
| ~ spl9_18 ),
inference(forward_demodulation,[],[f8190,f2469]) ).
fof(f8237,plain,
( composition(sF4,top) = join(sF4,composition(sF4,sF3))
| ~ spl9_12
| ~ spl9_18
| ~ spl9_21 ),
inference(forward_demodulation,[],[f8128,f1606]) ).
fof(f8243,plain,
( ! [X0] : complement(composition(sF4,complement(X0))) = join(X0,complement(composition(sF4,top)))
| ~ spl9_12
| ~ spl9_18 ),
inference(forward_demodulation,[],[f8199,f5875]) ).
fof(f8350,plain,
( ! [X0,X1] : join(X0,join(X1,complement(composition(sF4,top)))) = complement(composition(sF4,complement(join(X0,X1))))
| ~ spl9_12
| ~ spl9_18 ),
inference(superposition,[],[f2,f8243]) ).
fof(f8370,plain,
( join(sF3,complement(composition(sF4,top))) = join(sF2,complement(composition(sF4,complement(sF1))))
| ~ spl9_11
| ~ spl9_12
| ~ spl9_18 ),
inference(superposition,[],[f214,f8243]) ).
fof(f8375,plain,
( join(sF3,complement(composition(sF4,top))) = join(sF2,complement(composition(sF4,sF0)))
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18 ),
inference(forward_demodulation,[],[f8370,f876]) ).
fof(f8393,plain,
( ! [X0,X1] : complement(composition(sF4,complement(join(X0,X1)))) = join(X0,complement(composition(sF4,complement(X1))))
| ~ spl9_12
| ~ spl9_18 ),
inference(forward_demodulation,[],[f8350,f8243]) ).
fof(f8417,plain,
( join(sF2,complement(composition(sF4,sF0))) = complement(composition(sF4,complement(sF3)))
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18 ),
inference(forward_demodulation,[],[f8375,f8243]) ).
fof(f8444,plain,
( join(sF2,complement(composition(sF4,sF0))) = complement(composition(sF4,sF4))
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18 ),
inference(forward_demodulation,[],[f8417,f123]) ).
fof(f8515,plain,
! [X2,X0,X1] : join(composition(X1,top),composition(X0,complement(X2))) = join(composition(X1,X2),composition(join(X0,X1),complement(X2))),
inference(superposition,[],[f7135,f1]) ).
fof(f8565,plain,
( ! [X0] : join(composition(sF1,top),composition(one,complement(X0))) = join(composition(sF1,X0),composition(join(sF4,sF1),complement(X0)))
| ~ spl9_20 ),
inference(superposition,[],[f7135,f3188]) ).
fof(f8582,plain,
( ! [X0,X1] : join(composition(X0,one),composition(join(X0,X1),sF2)) = join(composition(X0,top),composition(X1,sF2))
| ~ spl9_10 ),
inference(superposition,[],[f7135,f179]) ).
fof(f8589,plain,
( ! [X0,X1] : join(composition(X0,sF2),composition(join(X0,X1),one)) = join(composition(X0,top),composition(X1,one))
| ~ spl9_22 ),
inference(superposition,[],[f7135,f3655]) ).
fof(f8674,plain,
( ! [X0,X1] : join(composition(X0,top),X1) = join(composition(X0,sF2),composition(join(X0,X1),one))
| ~ spl9_22 ),
inference(forward_demodulation,[],[f8589,f8]) ).
fof(f8676,plain,
( ! [X0,X1] : join(X0,composition(join(X0,X1),sF2)) = join(composition(X0,top),composition(X1,sF2))
| ~ spl9_10 ),
inference(forward_demodulation,[],[f8582,f8]) ).
fof(f8685,plain,
( ! [X0] : join(composition(sF1,X0),composition(join(sF4,sF1),complement(X0))) = join(composition(sF1,top),complement(X0))
| ~ spl9_20 ),
inference(forward_demodulation,[],[f8565,f944]) ).
fof(f8754,plain,
( ! [X0,X1] : join(composition(X0,top),X1) = join(composition(X0,sF2),join(X0,X1))
| ~ spl9_22 ),
inference(forward_demodulation,[],[f8674,f8]) ).
fof(f8760,plain,
( ! [X0] : join(sF1,complement(X0)) = join(composition(sF1,X0),composition(join(sF4,sF1),complement(X0)))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f8685,f6131]) ).
fof(f8809,plain,
( ! [X0,X1] : join(composition(X0,top),X1) = join(X0,join(X1,composition(X0,sF2)))
| ~ spl9_22 ),
inference(forward_demodulation,[],[f8754,f220]) ).
fof(f8813,plain,
( ! [X0] : join(sF1,complement(X0)) = join(composition(sF1,top),composition(sF4,complement(X0)))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f8760,f8515]) ).
fof(f8844,plain,
( ! [X0] : join(sF1,complement(X0)) = join(sF1,composition(sF4,complement(X0)))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f8813,f6131]) ).
fof(f8891,plain,
( ! [X0,X1] : join(X1,composition(join(X0,X1),sF2)) = join(composition(X1,top),composition(X0,sF2))
| ~ spl9_10 ),
inference(superposition,[],[f8676,f1]) ).
fof(f8943,plain,
( join(composition(sF1,top),composition(one,sF2)) = join(sF1,composition(join(sF4,sF1),sF2))
| ~ spl9_10
| ~ spl9_20 ),
inference(superposition,[],[f8676,f3188]) ).
fof(f9105,plain,
( join(sF1,composition(join(sF4,sF1),sF2)) = join(composition(sF1,top),sF2)
| ~ spl9_10
| ~ spl9_20 ),
inference(forward_demodulation,[],[f8943,f944]) ).
fof(f9190,plain,
( join(sF2,composition(sF1,top)) = join(sF1,composition(join(sF4,sF1),sF2))
| ~ spl9_10
| ~ spl9_20 ),
inference(forward_demodulation,[],[f9105,f1]) ).
fof(f9240,plain,
( join(sF2,composition(sF1,top)) = join(composition(sF1,top),composition(sF4,sF2))
| ~ spl9_10
| ~ spl9_20 ),
inference(forward_demodulation,[],[f9190,f8891]) ).
fof(f9266,plain,
( join(sF2,composition(sF1,top)) = join(composition(sF4,sF2),composition(sF1,top))
| ~ spl9_10
| ~ spl9_20 ),
inference(forward_demodulation,[],[f9240,f1]) ).
fof(f9279,plain,
( join(sF2,sF1) = join(composition(sF4,sF2),sF1)
| ~ spl9_7
| ~ spl9_10
| ~ spl9_12
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f9266,f6131]) ).
fof(f9290,plain,
( join(sF2,sF1) = join(sF1,composition(sF4,sF2))
| ~ spl9_7
| ~ spl9_10
| ~ spl9_12
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f9279,f1]) ).
fof(f9295,plain,
( sF3 = join(sF1,composition(sF4,sF2))
| ~ spl9_7
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f9290,f193]) ).
fof(f9296,plain,
( sF3 = join(sF1,composition(sF4,sF3))
| ~ spl9_7
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12
| ~ spl9_17
| ~ spl9_18
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(backward_demodulation,[],[f7747,f9295]) ).
fof(f9661,definition,
( spl9_39
<=> sF3 = join(sF1,composition(sF4,sF3)) ),
introduced(definition,[new_symbols(definition,[spl9_39])],[avatar_definition]) ).
fof(f9663,plain,
( sF3 = join(sF1,composition(sF4,sF3))
| ~ spl9_39 ),
inference(avatar_component_clause,[],[f9661]) ).
fof(f9664,plain,
( spl9_39
| ~ spl9_7
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12
| ~ spl9_17
| ~ spl9_18
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(avatar_split_clause,[],[f9296,f4987,f4447,f3186,f2996,f2011,f196,f191,f177,f109,f9661]) ).
fof(f9674,plain,
( complement(composition(sF4,sF3)) = join(complement(sF3),complement(join(complement(sF1),composition(sF4,sF3))))
| ~ spl9_12
| ~ spl9_39 ),
inference(superposition,[],[f397,f9663]) ).
fof(f9680,plain,
( join(composition(sF4,sF3),complement(sF1)) = join(composition(sF4,sF3),complement(sF3))
| ~ spl9_12
| ~ spl9_39 ),
inference(superposition,[],[f2607,f9663]) ).
fof(f9693,plain,
( join(composition(sF4,sF3),complement(sF1)) = join(complement(sF3),composition(sF4,sF3))
| ~ spl9_12
| ~ spl9_39 ),
inference(forward_demodulation,[],[f9680,f1]) ).
fof(f9699,plain,
( complement(composition(sF4,sF3)) = join(complement(sF3),complement(join(sF0,composition(sF4,sF3))))
| ~ spl9_12
| ~ spl9_14
| ~ spl9_39 ),
inference(forward_demodulation,[],[f9674,f876]) ).
fof(f9713,plain,
( join(sF4,composition(sF4,sF3)) = join(composition(sF4,sF3),complement(sF1))
| ~ spl9_8
| ~ spl9_12
| ~ spl9_39 ),
inference(forward_demodulation,[],[f9693,f123]) ).
fof(f9716,plain,
( complement(composition(sF4,sF3)) = join(sF4,complement(join(sF0,composition(sF4,sF3))))
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_39 ),
inference(forward_demodulation,[],[f9699,f123]) ).
fof(f9722,plain,
( join(sF4,composition(sF4,sF3)) = join(complement(sF1),composition(sF4,sF3))
| ~ spl9_8
| ~ spl9_12
| ~ spl9_39 ),
inference(forward_demodulation,[],[f9713,f1]) ).
fof(f9728,plain,
( join(sF4,composition(sF4,sF3)) = join(sF0,composition(sF4,sF3))
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_39 ),
inference(forward_demodulation,[],[f9722,f876]) ).
fof(f9732,plain,
( composition(sF4,top) = join(sF0,composition(sF4,sF3))
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_39 ),
inference(forward_demodulation,[],[f9728,f8237]) ).
fof(f9736,plain,
( join(sF4,complement(composition(sF4,top))) = complement(composition(sF4,sF3))
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_39 ),
inference(backward_demodulation,[],[f9716,f9732]) ).
fof(f9737,plain,
( complement(composition(sF4,sF3)) = join(sF4,complement(composition(sF4,sF2)))
| ~ spl9_8
| ~ spl9_10
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_39 ),
inference(forward_demodulation,[],[f9736,f2613]) ).
fof(f9928,plain,
( ! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(join(composition(sF4,X1),X0),X2))
| ~ spl9_18 ),
inference(superposition,[],[f2,f5797]) ).
fof(f9997,plain,
( ! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(composition(sF4,X1),join(X0,X2)))
| ~ spl9_18 ),
inference(forward_demodulation,[],[f9928,f2]) ).
fof(f10052,plain,
( ! [X2,X0,X1] : join(join(X0,X1),X2) = join(join(X0,X2),X1)
| ~ spl9_18 ),
inference(forward_demodulation,[],[f9997,f5797]) ).
fof(f10089,plain,
( ! [X2,X0,X1] : join(join(X0,X1),X2) = join(X0,join(X2,X1))
| ~ spl9_18 ),
inference(forward_demodulation,[],[f10052,f2]) ).
fof(f10104,plain,
( ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X0,join(X2,X1))
| ~ spl9_18 ),
inference(forward_demodulation,[],[f10089,f2]) ).
fof(f10176,definition,
( spl9_41
<=> sF0 = join(sF4,sF0) ),
introduced(definition,[new_symbols(definition,[spl9_41])],[avatar_definition]) ).
fof(f10178,plain,
( sF0 = join(sF4,sF0)
| ~ spl9_41 ),
inference(avatar_component_clause,[],[f10176]) ).
fof(f10179,plain,
( spl9_41
| ~ spl9_7
| ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14 ),
inference(avatar_split_clause,[],[f2976,f874,f196,f191,f177,f121,f109,f10176]) ).
fof(f10181,plain,
( composition(sF0,top) = join(sF0,composition(sF4,top))
| ~ spl9_1
| ~ spl9_41 ),
inference(superposition,[],[f85,f10178]) ).
fof(f10211,plain,
( composition(sF0,top) = join(sF0,composition(sF4,sF1))
| ~ spl9_1
| ~ spl9_18
| ~ spl9_23
| ~ spl9_41 ),
inference(forward_demodulation,[],[f10181,f7751]) ).
fof(f10218,plain,
( sF0 = join(sF0,composition(sF4,sF1))
| ~ spl9_1
| ~ spl9_18
| ~ spl9_23
| ~ spl9_41 ),
inference(forward_demodulation,[],[f10211,f50]) ).
fof(f10225,plain,
( sF0 = join(sF0,composition(sF4,top))
| ~ spl9_1
| ~ spl9_18
| ~ spl9_23
| ~ spl9_41 ),
inference(backward_demodulation,[],[f7751,f10218]) ).
fof(f10901,plain,
( ! [X0] : join(sF1,X0) = join(sF1,composition(sF4,X0))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(superposition,[],[f8844,f289]) ).
fof(f10912,plain,
( join(sF1,sk2) = join(sF1,composition(sF4,sk2))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_13
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(superposition,[],[f8844,f754]) ).
fof(f10962,plain,
( join(sF1,sk2) = join(sF1,sF5)
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_13
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f10912,f65]) ).
fof(f11054,plain,
( ! [X0] : join(sF1,complement(join(sF1,X0))) = join(sF1,complement(composition(sF4,X0)))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(superposition,[],[f2469,f10901]) ).
fof(f11068,plain,
( ! [X0] : join(sF1,complement(X0)) = join(sF1,complement(composition(sF4,X0)))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f11054,f2469]) ).
fof(f11260,definition,
( spl9_45
<=> join(sF1,sk2) = join(sF1,sF5) ),
introduced(definition,[new_symbols(definition,[spl9_45])],[avatar_definition]) ).
fof(f11262,plain,
( join(sF1,sk2) = join(sF1,sF5)
| ~ spl9_45 ),
inference(avatar_component_clause,[],[f11260]) ).
fof(f11263,plain,
( spl9_45
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_13
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(avatar_split_clause,[],[f10962,f4987,f4447,f3186,f2011,f752,f196,f109,f63,f11260]) ).
fof(f11278,plain,
( join(sF1,complement(join(sF1,sk2))) = join(sF1,complement(sF5))
| ~ spl9_12
| ~ spl9_45 ),
inference(superposition,[],[f2469,f11262]) ).
fof(f11292,plain,
( join(sF1,complement(sk2)) = join(sF1,complement(sF5))
| ~ spl9_12
| ~ spl9_45 ),
inference(forward_demodulation,[],[f11278,f2469]) ).
fof(f11308,plain,
( join(sF1,sF6) = join(sF1,complement(sF5))
| ~ spl9_6
| ~ spl9_12
| ~ spl9_45 ),
inference(forward_demodulation,[],[f11292,f89]) ).
fof(f11317,plain,
( join(sF6,sF1) = join(sF1,complement(sF5))
| ~ spl9_6
| ~ spl9_12
| ~ spl9_45 ),
inference(forward_demodulation,[],[f11308,f1]) ).
fof(f11320,plain,
( sF7 = join(sF1,complement(sF5))
| ~ spl9_6
| ~ spl9_9
| ~ spl9_12
| ~ spl9_45 ),
inference(forward_demodulation,[],[f11317,f174]) ).
fof(f11326,definition,
( spl9_46
<=> sF7 = join(sF1,complement(sF5)) ),
introduced(definition,[new_symbols(definition,[spl9_46])],[avatar_definition]) ).
fof(f11328,plain,
( sF7 = join(sF1,complement(sF5))
| ~ spl9_46 ),
inference(avatar_component_clause,[],[f11326]) ).
fof(f11329,plain,
( spl9_46
| ~ spl9_6
| ~ spl9_9
| ~ spl9_12
| ~ spl9_45 ),
inference(avatar_split_clause,[],[f11320,f11260,f196,f172,f87,f11326]) ).
fof(f11342,plain,
( complement(complement(sF5)) = join(complement(sF7),complement(join(complement(sF1),complement(sF5))))
| ~ spl9_12
| ~ spl9_46 ),
inference(superposition,[],[f397,f11328]) ).
fof(f11365,plain,
( complement(complement(sF5)) = join(complement(sF7),complement(join(sF0,complement(sF5))))
| ~ spl9_12
| ~ spl9_14
| ~ spl9_46 ),
inference(forward_demodulation,[],[f11342,f876]) ).
fof(f11381,plain,
( complement(complement(sF5)) = join(sF8,complement(join(sF0,complement(sF5))))
| ~ spl9_3
| ~ spl9_12
| ~ spl9_14
| ~ spl9_46 ),
inference(forward_demodulation,[],[f11365,f60]) ).
fof(f11393,plain,
( sF5 = join(sF8,complement(join(sF0,complement(sF5))))
| ~ spl9_3
| ~ spl9_12
| ~ spl9_14
| ~ spl9_46 ),
inference(forward_demodulation,[],[f11381,f289]) ).
fof(f11425,plain,
( complement(composition(sF4,sF0)) = join(sF1,complement(composition(sF4,sF0)))
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18 ),
inference(superposition,[],[f5875,f876]) ).
fof(f11509,plain,
( join(sF1,complement(sF0)) = complement(composition(sF4,sF0))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_14
| ~ spl9_17
| ~ spl9_18
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f11425,f11068]) ).
fof(f11529,plain,
( join(sF1,sF1) = complement(composition(sF4,sF0))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_14
| ~ spl9_17
| ~ spl9_18
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f11509,f111]) ).
fof(f11539,plain,
( sF1 = complement(composition(sF4,sF0))
| ~ spl9_7
| ~ spl9_12
| ~ spl9_14
| ~ spl9_17
| ~ spl9_18
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f11529,f977]) ).
fof(f11546,plain,
( join(sF2,sF1) = complement(composition(sF4,sF4))
| ~ spl9_7
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14
| ~ spl9_17
| ~ spl9_18
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(backward_demodulation,[],[f8444,f11539]) ).
fof(f11551,plain,
( sF3 = complement(composition(sF4,sF4))
| ~ spl9_7
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14
| ~ spl9_17
| ~ spl9_18
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(forward_demodulation,[],[f11546,f193]) ).
fof(f11561,definition,
( spl9_48
<=> sF3 = complement(composition(sF4,sF4)) ),
introduced(definition,[new_symbols(definition,[spl9_48])],[avatar_definition]) ).
fof(f11563,plain,
( sF3 = complement(composition(sF4,sF4))
| ~ spl9_48 ),
inference(avatar_component_clause,[],[f11561]) ).
fof(f11564,plain,
( spl9_48
| ~ spl9_7
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14
| ~ spl9_17
| ~ spl9_18
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27 ),
inference(avatar_split_clause,[],[f11551,f4987,f4447,f3186,f2996,f2011,f874,f196,f191,f121,f109,f11561]) ).
fof(f11576,plain,
( complement(sF3) = composition(sF4,sF4)
| ~ spl9_12
| ~ spl9_48 ),
inference(superposition,[],[f289,f11563]) ).
fof(f11596,plain,
( sF4 = composition(sF4,sF4)
| ~ spl9_8
| ~ spl9_12
| ~ spl9_48 ),
inference(forward_demodulation,[],[f11576,f123]) ).
fof(f11716,definition,
( spl9_50
<=> sF4 = composition(sF4,sF4) ),
introduced(definition,[new_symbols(definition,[spl9_50])],[avatar_definition]) ).
fof(f11718,plain,
( sF4 = composition(sF4,sF4)
| ~ spl9_50 ),
inference(avatar_component_clause,[],[f11716]) ).
fof(f11719,plain,
( spl9_50
| ~ spl9_8
| ~ spl9_12
| ~ spl9_48 ),
inference(avatar_split_clause,[],[f11596,f11561,f196,f121,f11716]) ).
fof(f11730,plain,
( ! [X0] : join(composition(sF4,X0),sF4) = composition(sF4,join(X0,sF4))
| ~ spl9_50 ),
inference(superposition,[],[f572,f11718]) ).
fof(f11740,plain,
( ! [X0] : join(sF4,composition(sF4,X0)) = composition(sF4,join(X0,sF4))
| ~ spl9_50 ),
inference(forward_demodulation,[],[f11730,f1]) ).
fof(f11753,plain,
( join(sF0,composition(sF4,sF2)) = join(sF0,join(sF4,composition(sF4,sF2)))
| ~ spl9_18
| ~ spl9_34
| ~ spl9_50 ),
inference(backward_demodulation,[],[f7748,f11740]) ).
fof(f11760,plain,
( join(sF0,composition(sF4,sF2)) = join(sF4,join(composition(sF4,sF2),sF0))
| ~ spl9_18
| ~ spl9_34
| ~ spl9_50 ),
inference(forward_demodulation,[],[f11753,f220]) ).
fof(f11764,plain,
( join(sF0,composition(sF4,sF2)) = join(sF4,join(sF0,composition(sF4,sF2)))
| ~ spl9_18
| ~ spl9_34
| ~ spl9_50 ),
inference(forward_demodulation,[],[f11760,f10104]) ).
fof(f11765,plain,
( join(sF0,composition(sF4,sF2)) = join(composition(sF4,top),sF0)
| ~ spl9_18
| ~ spl9_22
| ~ spl9_34
| ~ spl9_50 ),
inference(forward_demodulation,[],[f11764,f8809]) ).
fof(f11766,plain,
( join(sF0,composition(sF4,top)) = join(sF0,composition(sF4,sF2))
| ~ spl9_18
| ~ spl9_22
| ~ spl9_34
| ~ spl9_50 ),
inference(forward_demodulation,[],[f11765,f1]) ).
fof(f11767,plain,
( sF0 = join(sF0,composition(sF4,sF2))
| ~ spl9_1
| ~ spl9_18
| ~ spl9_22
| ~ spl9_23
| ~ spl9_34
| ~ spl9_41
| ~ spl9_50 ),
inference(forward_demodulation,[],[f11766,f10225]) ).
fof(f12563,definition,
( spl9_58
<=> composition(sF4,top) = join(sF5,composition(sF4,sF6)) ),
introduced(definition,[new_symbols(definition,[spl9_58])],[avatar_definition]) ).
fof(f12565,plain,
( composition(sF4,top) = join(sF5,composition(sF4,sF6))
| ~ spl9_58 ),
inference(avatar_component_clause,[],[f12563]) ).
fof(f12566,plain,
( spl9_58
| ~ spl9_4
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f1429,f87,f63,f12563]) ).
fof(f12577,plain,
( complement(sF5) = join(complement(sF5),complement(composition(sF4,top)))
| ~ spl9_12
| ~ spl9_58 ),
inference(superposition,[],[f2437,f12565]) ).
fof(f12593,plain,
( complement(sF5) = complement(composition(sF4,complement(complement(sF5))))
| ~ spl9_12
| ~ spl9_18
| ~ spl9_58 ),
inference(forward_demodulation,[],[f12577,f8243]) ).
fof(f12608,plain,
( complement(sF5) = complement(composition(sF4,sF5))
| ~ spl9_12
| ~ spl9_18
| ~ spl9_58 ),
inference(forward_demodulation,[],[f12593,f289]) ).
fof(f12632,definition,
( spl9_59
<=> complement(sF5) = complement(composition(sF4,sF5)) ),
introduced(definition,[new_symbols(definition,[spl9_59])],[avatar_definition]) ).
fof(f12634,plain,
( complement(sF5) = complement(composition(sF4,sF5))
| ~ spl9_59 ),
inference(avatar_component_clause,[],[f12632]) ).
fof(f12635,plain,
( spl9_59
| ~ spl9_12
| ~ spl9_18
| ~ spl9_58 ),
inference(avatar_split_clause,[],[f12608,f12563,f2996,f196,f12632]) ).
fof(f12643,plain,
( top = join(composition(sF4,sF5),complement(sF5))
| ~ spl9_59 ),
inference(superposition,[],[f15,f12634]) ).
fof(f12670,plain,
( top = join(complement(sF5),composition(sF4,sF5))
| ~ spl9_59 ),
inference(forward_demodulation,[],[f12643,f1]) ).
fof(f12694,plain,
( top = join(complement(sF5),composition(sF4,top))
| ~ spl9_18
| ~ spl9_59 ),
inference(forward_demodulation,[],[f12670,f7771]) ).
fof(f19185,plain,
( complement(composition(sF4,complement(one))) = join(sF4,complement(composition(sF4,complement(one))))
| ~ spl9_12
| ~ spl9_18 ),
inference(superposition,[],[f8393,f2998]) ).
fof(f19279,plain,
( complement(composition(sF4,sF2)) = join(sF4,complement(composition(sF4,sF2)))
| ~ spl9_10
| ~ spl9_12
| ~ spl9_18 ),
inference(forward_demodulation,[],[f19185,f179]) ).
fof(f19396,plain,
( complement(composition(sF4,sF3)) = complement(composition(sF4,sF2))
| ~ spl9_8
| ~ spl9_10
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_39 ),
inference(forward_demodulation,[],[f19279,f9737]) ).
fof(f19697,definition,
( spl9_67
<=> complement(composition(sF4,sF3)) = complement(composition(sF4,sF2)) ),
introduced(definition,[new_symbols(definition,[spl9_67])],[avatar_definition]) ).
fof(f19699,plain,
( complement(composition(sF4,sF3)) = complement(composition(sF4,sF2))
| ~ spl9_67 ),
inference(avatar_component_clause,[],[f19697]) ).
fof(f19700,plain,
( spl9_67
| ~ spl9_8
| ~ spl9_10
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_39 ),
inference(avatar_split_clause,[],[f19396,f9661,f3516,f2996,f874,f196,f177,f121,f19697]) ).
fof(f19713,plain,
( composition(sF4,sF3) = complement(complement(composition(sF4,sF2)))
| ~ spl9_12
| ~ spl9_67 ),
inference(superposition,[],[f289,f19699]) ).
fof(f19737,plain,
( composition(sF4,sF2) = composition(sF4,sF3)
| ~ spl9_12
| ~ spl9_67 ),
inference(forward_demodulation,[],[f19713,f289]) ).
fof(f19749,plain,
( composition(sF4,top) = join(sF0,composition(sF4,sF2))
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_39
| ~ spl9_67 ),
inference(backward_demodulation,[],[f9732,f19737]) ).
fof(f19779,plain,
( sF0 = composition(sF4,top)
| ~ spl9_1
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_22
| ~ spl9_23
| ~ spl9_34
| ~ spl9_39
| ~ spl9_41
| ~ spl9_50
| ~ spl9_67 ),
inference(forward_demodulation,[],[f19749,f11767]) ).
fof(f19849,plain,
( top = join(complement(sF5),sF0)
| ~ spl9_1
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_22
| ~ spl9_23
| ~ spl9_34
| ~ spl9_39
| ~ spl9_41
| ~ spl9_50
| ~ spl9_59
| ~ spl9_67 ),
inference(backward_demodulation,[],[f12694,f19779]) ).
fof(f19903,plain,
( top = join(sF0,complement(sF5))
| ~ spl9_1
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_22
| ~ spl9_23
| ~ spl9_34
| ~ spl9_39
| ~ spl9_41
| ~ spl9_50
| ~ spl9_59
| ~ spl9_67 ),
inference(forward_demodulation,[],[f19849,f1]) ).
fof(f19956,plain,
( sF5 = join(sF8,complement(top))
| ~ spl9_1
| ~ spl9_3
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_22
| ~ spl9_23
| ~ spl9_34
| ~ spl9_39
| ~ spl9_41
| ~ spl9_46
| ~ spl9_50
| ~ spl9_59
| ~ spl9_67 ),
inference(backward_demodulation,[],[f11393,f19903]) ).
fof(f20039,plain,
( sF5 = join(sF8,zero)
| ~ spl9_1
| ~ spl9_3
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_22
| ~ spl9_23
| ~ spl9_34
| ~ spl9_39
| ~ spl9_41
| ~ spl9_46
| ~ spl9_50
| ~ spl9_59
| ~ spl9_67 ),
inference(forward_demodulation,[],[f19956,f198]) ).
fof(f20103,plain,
( sF5 = join(zero,sF8)
| ~ spl9_1
| ~ spl9_3
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_22
| ~ spl9_23
| ~ spl9_34
| ~ spl9_39
| ~ spl9_41
| ~ spl9_46
| ~ spl9_50
| ~ spl9_59
| ~ spl9_67 ),
inference(forward_demodulation,[],[f20039,f1]) ).
fof(f20135,plain,
( sF5 = sF8
| ~ spl9_1
| ~ spl9_3
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_22
| ~ spl9_23
| ~ spl9_34
| ~ spl9_39
| ~ spl9_41
| ~ spl9_46
| ~ spl9_50
| ~ spl9_59
| ~ spl9_67 ),
inference(forward_demodulation,[],[f20103,f1066]) ).
fof(f20154,plain,
( $false
| ~ spl9_1
| ~ spl9_3
| spl9_5
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_22
| ~ spl9_23
| ~ spl9_34
| ~ spl9_39
| ~ spl9_41
| ~ spl9_46
| ~ spl9_50
| ~ spl9_59
| ~ spl9_67 ),
inference(forward_subsumption_resolution,[],[f20135,f70]) ).
fof(f20155,plain,
( ~ spl9_1
| ~ spl9_3
| spl9_5
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_22
| ~ spl9_23
| ~ spl9_34
| ~ spl9_39
| ~ spl9_41
| ~ spl9_46
| ~ spl9_50
| ~ spl9_59
| ~ spl9_67 ),
inference(avatar_contradiction_clause,[],[f20154]) ).
cnf(s1,plain,
spl9_1,
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
spl9_3,
inference(sat_conversion,[],[f61]) ).
cnf(s4,plain,
spl9_4,
inference(sat_conversion,[],[f66]) ).
cnf(s5,plain,
~ spl9_5,
inference(sat_conversion,[],[f71]) ).
cnf(s6,plain,
spl9_6,
inference(sat_conversion,[],[f90]) ).
cnf(s7,plain,
spl9_7,
inference(sat_conversion,[],[f112]) ).
cnf(s8,plain,
spl9_8,
inference(sat_conversion,[],[f124]) ).
cnf(s9,plain,
spl9_9,
inference(sat_conversion,[],[f175]) ).
cnf(s10,plain,
spl9_10,
inference(sat_conversion,[],[f180]) ).
cnf(s11,plain,
spl9_11,
inference(sat_conversion,[],[f194]) ).
cnf(s12,plain,
spl9_12,
inference(sat_conversion,[],[f199]) ).
cnf(s13,plain,
( ~ spl9_6
| ~ spl9_12
| spl9_13 ),
inference(sat_conversion,[],[f755]) ).
cnf(s14,plain,
( ~ spl9_7
| ~ spl9_12
| spl9_14 ),
inference(sat_conversion,[],[f877]) ).
cnf(s16,plain,
( ~ spl9_1
| ~ spl9_12
| spl9_16 ),
inference(sat_conversion,[],[f1276]) ).
cnf(s17,plain,
( ~ spl9_12
| spl9_17 ),
inference(sat_conversion,[],[f2014]) ).
cnf(s18,plain,
( ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12
| spl9_18 ),
inference(sat_conversion,[],[f2999]) ).
cnf(s20,plain,
( ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12
| spl9_20 ),
inference(sat_conversion,[],[f3189]) ).
cnf(s21,plain,
( ~ spl9_8
| ~ spl9_12
| spl9_21 ),
inference(sat_conversion,[],[f3519]) ).
cnf(s22,plain,
( ~ spl9_10
| ~ spl9_12
| spl9_22 ),
inference(sat_conversion,[],[f3656]) ).
cnf(s23,plain,
( ~ spl9_7
| spl9_23 ),
inference(sat_conversion,[],[f3827]) ).
cnf(s25,plain,
( ~ spl9_12
| spl9_25 ),
inference(sat_conversion,[],[f4450]) ).
cnf(s27,plain,
( ~ spl9_16
| spl9_27 ),
inference(sat_conversion,[],[f4990]) ).
cnf(s34,plain,
( ~ spl9_8
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14
| spl9_34 ),
inference(sat_conversion,[],[f6463]) ).
cnf(s39,plain,
( ~ spl9_7
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12
| ~ spl9_17
| ~ spl9_18
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27
| spl9_39 ),
inference(sat_conversion,[],[f9664]) ).
cnf(s41,plain,
( ~ spl9_7
| ~ spl9_8
| ~ spl9_10
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14
| spl9_41 ),
inference(sat_conversion,[],[f10179]) ).
cnf(s45,plain,
( ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_13
| ~ spl9_17
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27
| spl9_45 ),
inference(sat_conversion,[],[f11263]) ).
cnf(s46,plain,
( ~ spl9_6
| ~ spl9_9
| ~ spl9_12
| ~ spl9_45
| spl9_46 ),
inference(sat_conversion,[],[f11329]) ).
cnf(s48,plain,
( ~ spl9_7
| ~ spl9_8
| ~ spl9_11
| ~ spl9_12
| ~ spl9_14
| ~ spl9_17
| ~ spl9_18
| ~ spl9_20
| ~ spl9_25
| ~ spl9_27
| spl9_48 ),
inference(sat_conversion,[],[f11564]) ).
cnf(s50,plain,
( ~ spl9_8
| ~ spl9_12
| ~ spl9_48
| spl9_50 ),
inference(sat_conversion,[],[f11719]) ).
cnf(s58,plain,
( ~ spl9_4
| ~ spl9_6
| spl9_58 ),
inference(sat_conversion,[],[f12566]) ).
cnf(s59,plain,
( ~ spl9_12
| ~ spl9_18
| ~ spl9_58
| spl9_59 ),
inference(sat_conversion,[],[f12635]) ).
cnf(s67,plain,
( ~ spl9_8
| ~ spl9_10
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_39
| spl9_67 ),
inference(sat_conversion,[],[f19700]) ).
cnf(s68,plain,
( ~ spl9_1
| ~ spl9_3
| spl9_5
| ~ spl9_8
| ~ spl9_12
| ~ spl9_14
| ~ spl9_18
| ~ spl9_21
| ~ spl9_22
| ~ spl9_23
| ~ spl9_34
| ~ spl9_39
| ~ spl9_41
| ~ spl9_46
| ~ spl9_50
| ~ spl9_59
| ~ spl9_67 ),
inference(sat_conversion,[],[f20155]) ).
cnf(s70,plain,
spl9_25,
inference(rat,[],[s25,s12]) ).
cnf(s71,plain,
spl9_17,
inference(rat,[],[s17,s12]) ).
cnf(s75,plain,
spl9_22,
inference(rat,[],[s22,s12,s10]) ).
cnf(s80,plain,
spl9_21,
inference(rat,[],[s21,s12,s8]) ).
cnf(s81,plain,
spl9_20,
inference(rat,[],[s20,s10,s12,s11,s8]) ).
cnf(s82,plain,
spl9_18,
inference(rat,[],[s18,s10,s12,s11,s8]) ).
cnf(s85,plain,
spl9_23,
inference(rat,[],[s23,s7]) ).
cnf(s86,plain,
spl9_14,
inference(rat,[],[s14,s12,s7]) ).
cnf(s87,plain,
spl9_34,
inference(rat,[],[s34,s8,s11,s12,s86]) ).
cnf(s88,plain,
spl9_41,
inference(rat,[],[s41,s7,s8,s12,s11,s10,s86]) ).
cnf(s90,plain,
spl9_13,
inference(rat,[],[s13,s12,s6]) ).
cnf(s91,plain,
spl9_58,
inference(rat,[],[s58,s6,s4]) ).
cnf(s94,plain,
spl9_59,
inference(rat,[],[s59,s82,s12,s91]) ).
cnf(s104,plain,
spl9_16,
inference(rat,[],[s16,s12,s1]) ).
cnf(s105,plain,
spl9_27,
inference(rat,[],[s27,s104]) ).
cnf(s109,plain,
spl9_39,
inference(rat,[],[s39,s7,s82,s70,s81,s10,s71,s12,s11,s105]) ).
cnf(s111,plain,
spl9_48,
inference(rat,[],[s48,s86,s7,s70,s81,s82,s71,s8,s12,s11,s105]) ).
cnf(s113,plain,
spl9_45,
inference(rat,[],[s45,s4,s90,s70,s81,s71,s7,s12,s105]) ).
cnf(s115,plain,
spl9_67,
inference(rat,[],[s67,s86,s82,s80,s8,s10,s12,s109]) ).
cnf(s117,plain,
spl9_50,
inference(rat,[],[s50,s8,s12,s111]) ).
cnf(s119,plain,
spl9_46,
inference(rat,[],[s46,s6,s9,s12,s113]) ).
cnf(s123,plain,
$false,
inference(rat,[],[s68,s115,s94,s109,s1,s88,s3,s87,s85,s75,s80,s82,s86,s12,s8,s5,s117,s119]) ).
fof(f20237,plain,
$false,
inference(avatar_sat_refutation,[],[s123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL020-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 22:49:40 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.80/3.36 % (1859871)Detected a unit-equality problem, will run specialized UEQ schedule.
% 17.80/3.36 % (1859880)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=25296927:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 17.80/3.36 % (1859876)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3829532539:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 17.80/3.36 % (1859879)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=810880206:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 17.80/3.36 % (1859878)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=24961988:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 17.80/3.36 % (1859882)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1404480513:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 17.80/3.36 % (1859877)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=709364492:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 17.80/3.36 % (1859881)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=335214524:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 17.80/3.36 % (1859880)Instruction limit reached!
% 17.80/3.36 % (1859880)------------------------------
% 17.80/3.36 % (1859880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.80/3.36 % (1859880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.80/3.36 % (1859880)CaDiCaL version: 2.1.3
% 17.80/3.36 % (1859880)Termination reason: Instruction limit
% 17.80/3.36 % (1859880)Termination phase: Saturation
% 17.80/3.36 % (1859880)Time elapsed: 0.057 s
% 17.80/3.36 % (1859880)Peak memory usage: 90 MB
% 17.80/3.36 % (1859880)Instructions burned: 184 (million)
% 17.80/3.36 % (1859879)Instruction limit reached!
% 17.80/3.36 % (1859879)------------------------------
% 17.80/3.36 % (1859879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.80/3.36 % (1859879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.80/3.36 % (1859879)CaDiCaL version: 2.1.3
% 17.80/3.36 % (1859879)Termination reason: Instruction limit
% 17.80/3.36 % (1859879)Termination phase: Saturation
% 17.80/3.36 % (1859879)Time elapsed: 0.085 s
% 17.80/3.36 % (1859879)Peak memory usage: 89 MB
% 17.80/3.36 % (1859879)Instructions burned: 136 (million)
% 17.80/3.36 % (1859890)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=265082181:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 17.80/3.36 % (1859881)Instruction limit reached!
% 17.80/3.36 % (1859881)------------------------------
% 17.80/3.36 % (1859881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.80/3.36 % (1859881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.80/3.36 % (1859881)CaDiCaL version: 2.1.3
% 17.80/3.36 % (1859881)Termination reason: Instruction limit
% 17.80/3.36 % (1859881)Termination phase: Saturation
% 17.80/3.36 % (1859881)Time elapsed: 0.171 s
% 17.80/3.36 % (1859881)Peak memory usage: 90 MB
% 17.80/3.36 % (1859881)Instructions burned: 258 (million)
% 17.80/3.36 % (1859891)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1301563483:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 17.80/3.36 % (1859893)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=939680435:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 17.80/3.36 % (1859893)Instruction limit reached!
% 17.80/3.36 % (1859893)------------------------------
% 17.80/3.36 % (1859893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.80/3.36 % (1859893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.80/3.36 % (1859893)CaDiCaL version: 2.1.3
% 17.80/3.36 % (1859893)Termination reason: Instruction limit
% 17.80/3.36 % (1859893)Termination phase: Saturation
% 17.80/3.36 % (1859893)Time elapsed: 0.123 s
% 17.80/3.36 % (1859893)Peak memory usage: 92 MB
% 17.80/3.36 % (1859893)Instructions burned: 216 (million)
% 17.80/3.36 % (1859896)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=4028166754:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 17.80/3.36 % (1859882)Instruction limit reached!
% 17.80/3.36 % (1859882)------------------------------
% 17.80/3.36 % (1859882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.80/3.36 % (1859882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.80/3.36 % (1859882)CaDiCaL version: 2.1.3
% 17.80/3.36 % (1859882)Termination reason: Instruction limit
% 17.80/3.36 % (1859882)Termination phase: Saturation
% 17.80/3.36 % (1859882)Time elapsed: 0.650 s
% 17.80/3.36 % (1859882)Peak memory usage: 99 MB
% 17.80/3.36 % (1859882)Instructions burned: 1189 (million)
% 17.80/3.36 % (1859898)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2608888934:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 17.80/3.36 % (1859896)Instruction limit reached!
% 17.80/3.36 % (1859896)------------------------------
% 17.80/3.36 % (1859896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.80/3.36 % (1859896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.80/3.36 % (1859896)CaDiCaL version: 2.1.3
% 17.80/3.36 % (1859896)Termination reason: Instruction limit
% 17.80/3.36 % (1859896)Termination phase: Saturation
% 17.80/3.36 % (1859896)Time elapsed: 0.198 s
% 17.80/3.36 % (1859896)Peak memory usage: 93 MB
% 17.80/3.36 % (1859896)Instructions burned: 318 (million)
% 17.80/3.36 % (1859900)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3439443855:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 17.80/3.36 % (1859890)Instruction limit reached!
% 17.80/3.36 % (1859890)------------------------------
% 17.80/3.36 % (1859890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.80/3.36 % (1859890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.80/3.36 % (1859890)CaDiCaL version: 2.1.3
% 17.80/3.36 % (1859890)Termination reason: Instruction limit
% 17.80/3.36 % (1859890)Termination phase: Saturation
% 17.80/3.36 % (1859890)Time elapsed: 1.121 s
% 17.80/3.36 % (1859890)Peak memory usage: 141 MB
% 17.80/3.36 % (1859890)Instructions burned: 2051 (million)
% 17.80/3.36 % (1859902)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=2922105846:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2985 on theBenchmark for (2985ds/14534Mi)
% 17.80/3.36 % (1859876)First to succeed.
% 17.80/3.36 % (1859876)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1859871"
% 17.80/3.36 % (1859876)Refutation found. Thanks to Tanya!
% 17.80/3.36 % SZS status Unsatisfiable for theBenchmark
% 17.80/3.36 % SZS output start Proof for theBenchmark
% See solution above
% 18.44/3.56 % (1859876)------------------------------
% 18.44/3.56 % (1859876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.44/3.56 % (1859876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.44/3.56 % (1859876)CaDiCaL version: 2.1.3
% 18.44/3.56 % (1859876)Termination reason: Refutation
% 18.44/3.56 % (1859876)Time elapsed: 2.091 s
% 18.44/3.56 % (1859876)Peak memory usage: 154 MB
% 18.44/3.56 % (1859876)Instructions burned: 3289 (million)
% 18.44/3.56 % (1859876)------------------------------
% 18.44/3.56 % (1859876)------------------------------
% 18.44/3.56 % (1859871)Success in time 2.523 s
% 18.44/3.56 % Vampire exiting
%------------------------------------------------------------------------------