%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL032-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:33:58 PM UTC 2026
% Result : Unsatisfiable 15.26s 3.38s
% Output : Refutation 18.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 48
% Syntax : Number of formulae : 289 ( 135 unt; 35 def)
% Number of atoms : 622 ( 229 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 649 ( 316 ~; 310 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 18 con; 0-2 aty)
% Number of variables : 168 ( 0 sgn 168 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f17,negated_conjecture,
join(composition(sk1,meet(sk2,sk3)),meet(composition(sk1,sk2),composition(sk1,sk3))) != meet(composition(sk1,sk2),composition(sk1,sk3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
meet(composition(sk1,sk2),composition(sk1,sk3)) != join(composition(sk1,meet(sk2,sk3)),meet(composition(sk1,sk2),composition(sk1,sk3))),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f20,plain,
complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))) != join(composition(sk1,complement(join(complement(sk2),complement(sk3)))),complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3))))),
inference(definition_unfolding,[],[f18,f6,f6,f6]) ).
fof(f21,definition,
sF0 = composition(sk1,sk2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f22,plain,
composition(sk1,sk2) = sF0,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF1 = complement(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f24,plain,
complement(sF0) = sF1,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF2 = composition(sk1,sk3),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f26,plain,
composition(sk1,sk3) = sF2,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF3 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f28,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF4 = join(sF1,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f30,plain,
join(sF1,sF3) = sF4,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f32,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF6 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f34,plain,
complement(sk2) = sF6,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF7 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f36,plain,
complement(sk3) = sF7,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF8 = join(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f38,plain,
join(sF6,sF7) = sF8,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f40,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF10 = composition(sk1,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f42,plain,
composition(sk1,sF9) = sF10,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF11 = join(sF10,sF5),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f44,plain,
join(sF10,sF5) = sF11,
inference(reorient_equations,[],[f43]) ).
fof(f45,plain,
sF5 != sF11,
inference(definition_folding,[],[f20,f44,f32,f30,f28,f26,f24,f22,f42,f40,f38,f36,f34,f32,f30,f28,f26,f24,f22]) ).
fof(f46,plain,
zero = complement(top),
inference(backward_demodulation,[],[f19,f15]) ).
fof(f56,definition,
( spl12_1
<=> complement(sF4) = sF5 ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f58,plain,
( complement(sF4) = sF5
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,plain,
spl12_1,
inference(avatar_split_clause,[],[f32,f56]) ).
fof(f61,definition,
( spl12_2
<=> sF5 = sF11 ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f63,plain,
( sF5 != sF11
| spl12_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,plain,
~ spl12_2,
inference(avatar_split_clause,[],[f45,f61]) ).
fof(f68,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f4,f1]) ).
fof(f81,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(forward_demodulation,[],[f68,f1]) ).
fof(f89,definition,
( spl12_3
<=> join(sF10,sF5) = sF11 ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f91,plain,
( join(sF10,sF5) = sF11
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
spl12_3,
inference(avatar_split_clause,[],[f44,f89]) ).
fof(f94,definition,
( spl12_4
<=> complement(sk2) = sF6 ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f96,plain,
( complement(sk2) = sF6
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
spl12_4,
inference(avatar_split_clause,[],[f34,f94]) ).
fof(f103,definition,
( spl12_5
<=> complement(sk3) = sF7 ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f105,plain,
( complement(sk3) = sF7
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
spl12_5,
inference(avatar_split_clause,[],[f36,f103]) ).
fof(f124,definition,
( spl12_6
<=> complement(sF0) = sF1 ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
fof(f126,plain,
( complement(sF0) = sF1
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
spl12_6,
inference(avatar_split_clause,[],[f24,f124]) ).
fof(f139,definition,
( spl12_7
<=> complement(sF2) = sF3 ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f141,plain,
( complement(sF2) = sF3
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
spl12_7,
inference(avatar_split_clause,[],[f28,f139]) ).
fof(f154,definition,
( spl12_8
<=> complement(sF8) = sF9 ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
fof(f156,plain,
( complement(sF8) = sF9
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f157,plain,
spl12_8,
inference(avatar_split_clause,[],[f40,f154]) ).
fof(f169,definition,
( spl12_9
<=> composition(sk1,sk2) = sF0 ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f171,plain,
( composition(sk1,sk2) = sF0
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
spl12_9,
inference(avatar_split_clause,[],[f22,f169]) ).
fof(f188,definition,
( spl12_10
<=> composition(sk1,sk3) = sF2 ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
fof(f190,plain,
( composition(sk1,sk3) = sF2
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f191,plain,
spl12_10,
inference(avatar_split_clause,[],[f26,f188]) ).
fof(f203,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(f206,plain,
( ! [X0] : join(sF10,join(sF5,X0)) = join(sF11,X0)
| ~ spl12_3 ),
inference(superposition,[],[f2,f91]) ).
fof(f210,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f212,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(X2,complement(join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f203,f210]) ).
fof(f238,plain,
! [X0] : join(complement(join(complement(X0),complement(complement(complement(X0))))),complement(top)) = X0,
inference(superposition,[],[f4,f15]) ).
fof(f239,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f238,f1]) ).
fof(f243,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f239,f46]) ).
fof(f245,definition,
( spl12_11
<=> join(sF6,sF7) = sF8 ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
fof(f247,plain,
( join(sF6,sF7) = sF8
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,plain,
spl12_11,
inference(avatar_split_clause,[],[f38,f245]) ).
fof(f251,definition,
( spl12_12
<=> join(sF1,sF3) = sF4 ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
fof(f253,plain,
( join(sF1,sF3) = sF4
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,plain,
spl12_12,
inference(avatar_split_clause,[],[f30,f251]) ).
fof(f257,definition,
( spl12_13
<=> composition(sk1,sF9) = sF10 ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
fof(f259,plain,
( composition(sk1,sF9) = sF10
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f260,plain,
spl12_13,
inference(avatar_split_clause,[],[f42,f257]) ).
fof(f268,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f271,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(f280,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f271,f12]) ).
fof(f290,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f280,f11]) ).
fof(f293,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f290,f11]) ).
fof(f295,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f293,f12]) ).
fof(f310,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f295]) ).
fof(f322,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f310,f10]) ).
fof(f346,plain,
( ! [X0] : composition(sk1,join(sk3,X0)) = join(sF2,composition(sk1,X0))
| ~ spl12_10 ),
inference(superposition,[],[f322,f190]) ).
fof(f347,plain,
( ! [X0] : composition(sk1,join(sF9,X0)) = join(sF10,composition(sk1,X0))
| ~ spl12_13 ),
inference(superposition,[],[f322,f259]) ).
fof(f361,plain,
! [X2,X0,X1] : join(composition(X0,X2),composition(X0,X1)) = composition(X0,join(X1,X2)),
inference(superposition,[],[f1,f322]) ).
fof(f362,plain,
! [X2,X0,X1] : composition(X0,join(X2,X1)) = composition(X0,join(X1,X2)),
inference(forward_demodulation,[],[f361,f322]) ).
fof(f416,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f81,f15]) ).
fof(f424,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f416,f1]) ).
fof(f441,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f424,f1]) ).
fof(f448,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f441,f46]) ).
fof(f454,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f243,f448]) ).
fof(f457,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f448,f454]) ).
fof(f462,plain,
( sk2 = complement(sF6)
| ~ spl12_4 ),
inference(superposition,[],[f454,f96]) ).
fof(f463,plain,
( sk3 = complement(sF7)
| ~ spl12_5 ),
inference(superposition,[],[f454,f105]) ).
fof(f464,plain,
( sF0 = complement(sF1)
| ~ spl12_6 ),
inference(superposition,[],[f454,f126]) ).
fof(f465,plain,
( sF2 = complement(sF3)
| ~ spl12_7 ),
inference(superposition,[],[f454,f141]) ).
fof(f468,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,complement(X1))),complement(join(X0,X1))),
inference(superposition,[],[f4,f454]) ).
fof(f473,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f81,f454]) ).
fof(f479,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(forward_demodulation,[],[f468,f1]) ).
fof(f489,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f479,f1]) ).
fof(f596,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),join(complement(X1),X0)))),
inference(superposition,[],[f4,f473]) ).
fof(f605,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(X0,join(complement(join(X0,X1)),complement(X1))))),
inference(forward_demodulation,[],[f596,f210]) ).
fof(f623,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f605,f1]) ).
fof(f638,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f623,f454]) ).
fof(f671,definition,
( spl12_14
<=> sk2 = complement(sF6) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
fof(f673,plain,
( sk2 = complement(sF6)
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f674,plain,
( spl12_14
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f462,f94,f671]) ).
fof(f676,definition,
( spl12_15
<=> sk3 = complement(sF7) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
fof(f678,plain,
( sk3 = complement(sF7)
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f676]) ).
fof(f679,plain,
( spl12_15
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f463,f103,f676]) ).
fof(f681,definition,
( spl12_16
<=> zero = complement(top) ),
introduced(definition,[new_symbols(definition,[spl12_16])],[avatar_definition]) ).
fof(f683,plain,
( zero = complement(top)
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f684,plain,
spl12_16,
inference(avatar_split_clause,[],[f46,f681]) ).
fof(f699,plain,
( complement(sF7) = join(complement(sF8),complement(join(sF7,complement(sF6))))
| ~ spl12_11 ),
inference(superposition,[],[f489,f247]) ).
fof(f718,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(join(complement(join(X0,complement(X1))),join(X1,X0))),complement(complement(X0))),
inference(superposition,[],[f473,f489]) ).
fof(f728,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(complement(join(X0,complement(X1))),join(X1,X0)))),
inference(forward_demodulation,[],[f718,f1]) ).
fof(f739,plain,
( complement(sF7) = join(complement(sF8),complement(join(sF7,sk2)))
| ~ spl12_11
| ~ spl12_14 ),
inference(forward_demodulation,[],[f699,f673]) ).
fof(f751,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(join(X1,X0),complement(join(X0,complement(X1)))))),
inference(forward_demodulation,[],[f728,f1]) ).
fof(f759,plain,
( complement(sF7) = join(sF9,complement(join(sF7,sk2)))
| ~ spl12_8
| ~ spl12_11
| ~ spl12_14 ),
inference(forward_demodulation,[],[f739,f156]) ).
fof(f769,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f751,f2]) ).
fof(f775,plain,
( sk3 = join(sF9,complement(join(sF7,sk2)))
| ~ spl12_8
| ~ spl12_11
| ~ spl12_14
| ~ spl12_15 ),
inference(forward_demodulation,[],[f759,f678]) ).
fof(f785,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f769,f454]) ).
fof(f798,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f785,f454]) ).
fof(f812,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f268,f8]) ).
fof(f828,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f812,f10]) ).
fof(f842,plain,
! [X0] : complement(X0) = join(complement(composition(one,X0)),complement(X0)),
inference(superposition,[],[f14,f828]) ).
fof(f852,plain,
one = converse(one),
inference(superposition,[],[f8,f828]) ).
fof(f855,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f828,f852]) ).
fof(f864,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(forward_demodulation,[],[f842,f1]) ).
fof(f871,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f864,f855]) ).
fof(f925,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(X1,complement(top))),
inference(superposition,[],[f212,f15]) ).
fof(f957,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(complement(join(complement(X0),complement(X0))),X1)),
inference(forward_demodulation,[],[f925,f210]) ).
fof(f990,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(complement(complement(X0)),X1)),
inference(forward_demodulation,[],[f957,f871]) ).
fof(f1008,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X0,X1)),
inference(forward_demodulation,[],[f990,f454]) ).
fof(f1021,plain,
( ! [X0,X1] : join(X0,X1) = join(zero,join(X0,X1))
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1008,f683]) ).
fof(f1043,plain,
( composition(sk1,join(sk3,sF9)) = join(sF2,sF10)
| ~ spl12_10
| ~ spl12_13 ),
inference(superposition,[],[f346,f259]) ).
fof(f1053,plain,
( join(sF2,sF10) = composition(sk1,join(sF9,sk3))
| ~ spl12_10
| ~ spl12_13 ),
inference(forward_demodulation,[],[f1043,f362]) ).
fof(f1091,plain,
( composition(sk1,join(sF9,sk2)) = join(sF10,sF0)
| ~ spl12_9
| ~ spl12_13 ),
inference(superposition,[],[f347,f171]) ).
fof(f1102,plain,
( composition(sk1,join(sF9,sk2)) = join(sF0,sF10)
| ~ spl12_9
| ~ spl12_13 ),
inference(forward_demodulation,[],[f1091,f1]) ).
fof(f1126,plain,
! [X0] : complement(zero) = join(complement(complement(X0)),complement(join(zero,complement(complement(join(X0,X0)))))),
inference(superposition,[],[f479,f457]) ).
fof(f1129,plain,
! [X0] : complement(zero) = join(complement(complement(X0)),complement(join(zero,join(X0,X0)))),
inference(forward_demodulation,[],[f1126,f454]) ).
fof(f1134,plain,
( ! [X0] : complement(zero) = join(complement(complement(X0)),complement(join(X0,X0)))
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1129,f1021]) ).
fof(f1139,plain,
( ! [X0] : complement(zero) = join(X0,complement(join(X0,X0)))
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1134,f454]) ).
fof(f1162,plain,
( ! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(zero)),complement(join(complement(join(X0,X0)),complement(X0))))
| ~ spl12_16 ),
inference(superposition,[],[f489,f1139]) ).
fof(f1167,plain,
( ! [X0] : join(complement(complement(zero)),complement(join(complement(X0),join(complement(X0),complement(X0))))) = X0
| ~ spl12_16 ),
inference(superposition,[],[f4,f1139]) ).
fof(f1172,plain,
( ! [X0] : join(complement(complement(zero)),complement(join(complement(X0),complement(X0)))) = X0
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1167,f871]) ).
fof(f1177,plain,
( ! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(zero)),complement(join(complement(X0),complement(join(X0,X0)))))
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1162,f1]) ).
fof(f1189,plain,
( ! [X0] : join(complement(complement(zero)),complement(complement(X0))) = X0
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1172,f871]) ).
fof(f1194,plain,
( ! [X0] : complement(complement(join(X0,X0))) = join(zero,complement(join(complement(X0),complement(join(X0,X0)))))
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1177,f454]) ).
fof(f1210,plain,
( ! [X0] : join(complement(complement(zero)),X0) = X0
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1189,f454]) ).
fof(f1212,plain,
( ! [X0] : join(X0,X0) = join(zero,complement(join(complement(X0),complement(join(X0,X0)))))
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1194,f454]) ).
fof(f1230,plain,
( ! [X0] : join(zero,X0) = X0
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1210,f454]) ).
fof(f1237,plain,
( ! [X0] : complement(X0) = complement(join(X0,X0))
| ~ spl12_16 ),
inference(backward_demodulation,[],[f457,f1230]) ).
fof(f1240,plain,
( ! [X0] : join(X0,X0) = complement(join(complement(X0),complement(join(X0,X0))))
| ~ spl12_16 ),
inference(backward_demodulation,[],[f1212,f1230]) ).
fof(f1251,plain,
( ! [X0] : complement(join(complement(X0),complement(X0))) = join(X0,X0)
| ~ spl12_16 ),
inference(backward_demodulation,[],[f1240,f1237]) ).
fof(f1252,plain,
( ! [X0] : complement(complement(X0)) = join(X0,X0)
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1251,f1237]) ).
fof(f1253,plain,
( ! [X0] : join(X0,X0) = X0
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1252,f454]) ).
fof(f1272,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1))
| ~ spl12_16 ),
inference(superposition,[],[f2,f1253]) ).
fof(f1377,plain,
( ! [X0,X1] : join(X0,X1) = join(X1,join(X0,X1))
| ~ spl12_16 ),
inference(superposition,[],[f1272,f1]) ).
fof(f1384,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(X0))
| ~ spl12_16 ),
inference(superposition,[],[f1272,f479]) ).
fof(f1385,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0))
| ~ spl12_16 ),
inference(superposition,[],[f1272,f489]) ).
fof(f1421,plain,
( ! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0)))
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1385,f1]) ).
fof(f1422,plain,
( ! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1)))
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1384,f1]) ).
fof(f1433,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1))))
| ~ spl12_16 ),
inference(backward_demodulation,[],[f638,f1421]) ).
fof(f1437,plain,
( ! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1))))
| ~ spl12_16 ),
inference(backward_demodulation,[],[f798,f1433]) ).
fof(f1443,plain,
( ! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1)))
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1437,f1377]) ).
fof(f1489,plain,
( complement(sF1) = join(complement(sF1),complement(sF4))
| ~ spl12_12
| ~ spl12_16 ),
inference(superposition,[],[f1422,f253]) ).
fof(f1491,plain,
( complement(sF6) = join(complement(sF6),complement(sF8))
| ~ spl12_11
| ~ spl12_16 ),
inference(superposition,[],[f1422,f247]) ).
fof(f1510,plain,
( complement(sF6) = join(complement(sF6),sF9)
| ~ spl12_8
| ~ spl12_11
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1491,f156]) ).
fof(f1512,plain,
( complement(sF1) = join(complement(sF1),sF5)
| ~ spl12_1
| ~ spl12_12
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1489,f58]) ).
fof(f1524,plain,
( complement(sF6) = join(sF9,complement(sF6))
| ~ spl12_8
| ~ spl12_11
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1510,f1]) ).
fof(f1525,plain,
( complement(sF1) = join(sF5,complement(sF1))
| ~ spl12_1
| ~ spl12_12
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1512,f1]) ).
fof(f1534,plain,
( sk2 = join(sF9,sk2)
| ~ spl12_8
| ~ spl12_11
| ~ spl12_14
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1524,f673]) ).
fof(f1535,plain,
( sF0 = join(sF5,sF0)
| ~ spl12_1
| ~ spl12_6
| ~ spl12_12
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1525,f464]) ).
fof(f1541,plain,
( composition(sk1,sk2) = join(sF0,sF10)
| ~ spl12_8
| ~ spl12_9
| ~ spl12_11
| ~ spl12_13
| ~ spl12_14
| ~ spl12_16 ),
inference(backward_demodulation,[],[f1102,f1534]) ).
fof(f1542,plain,
( sF0 = join(sF0,sF5)
| ~ spl12_1
| ~ spl12_6
| ~ spl12_12
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1535,f1]) ).
fof(f1547,plain,
( sF0 = join(sF0,sF10)
| ~ spl12_8
| ~ spl12_9
| ~ spl12_11
| ~ spl12_13
| ~ spl12_14
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1541,f171]) ).
fof(f1553,plain,
( ! [X0,X1] : join(X1,complement(X0)) = join(X1,complement(join(X0,X1)))
| ~ spl12_16 ),
inference(superposition,[],[f1443,f1]) ).
fof(f1569,plain,
( join(sF1,complement(sF3)) = join(sF1,complement(sF4))
| ~ spl12_12
| ~ spl12_16 ),
inference(superposition,[],[f1443,f253]) ).
fof(f1604,plain,
( join(sF1,complement(sF3)) = join(sF1,sF5)
| ~ spl12_1
| ~ spl12_12
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1569,f58]) ).
fof(f1631,plain,
( join(sF1,sF2) = join(sF1,sF5)
| ~ spl12_1
| ~ spl12_7
| ~ spl12_12
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1604,f465]) ).
fof(f1708,plain,
( join(sF7,complement(sF6)) = join(sF7,complement(sF8))
| ~ spl12_11
| ~ spl12_16 ),
inference(superposition,[],[f1553,f247]) ).
fof(f1743,plain,
( join(sF7,complement(sF6)) = join(sF7,sF9)
| ~ spl12_8
| ~ spl12_11
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1708,f156]) ).
fof(f1769,plain,
( join(sF7,sk2) = join(sF7,sF9)
| ~ spl12_8
| ~ spl12_11
| ~ spl12_14
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1743,f673]) ).
fof(f1789,plain,
( sk3 = join(sF9,complement(join(sF7,sF9)))
| ~ spl12_8
| ~ spl12_11
| ~ spl12_14
| ~ spl12_15
| ~ spl12_16 ),
inference(backward_demodulation,[],[f775,f1769]) ).
fof(f1803,plain,
( sk3 = join(sF9,complement(sF7))
| ~ spl12_8
| ~ spl12_11
| ~ spl12_14
| ~ spl12_15
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1789,f1553]) ).
fof(f1813,plain,
( sk3 = join(sF9,sk3)
| ~ spl12_8
| ~ spl12_11
| ~ spl12_14
| ~ spl12_15
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1803,f678]) ).
fof(f1822,plain,
( composition(sk1,sk3) = join(sF2,sF10)
| ~ spl12_8
| ~ spl12_10
| ~ spl12_11
| ~ spl12_13
| ~ spl12_14
| ~ spl12_15
| ~ spl12_16 ),
inference(backward_demodulation,[],[f1053,f1813]) ).
fof(f1829,plain,
( sF2 = join(sF2,sF10)
| ~ spl12_8
| ~ spl12_10
| ~ spl12_11
| ~ spl12_13
| ~ spl12_14
| ~ spl12_15
| ~ spl12_16 ),
inference(forward_demodulation,[],[f1822,f190]) ).
fof(f2078,definition,
( spl12_19
<=> sF0 = complement(sF1) ),
introduced(definition,[new_symbols(definition,[spl12_19])],[avatar_definition]) ).
fof(f2080,plain,
( sF0 = complement(sF1)
| ~ spl12_19 ),
inference(avatar_component_clause,[],[f2078]) ).
fof(f2081,plain,
( spl12_19
| ~ spl12_6 ),
inference(avatar_split_clause,[],[f464,f124,f2078]) ).
fof(f3385,definition,
( spl12_24
<=> sF0 = join(sF0,sF5) ),
introduced(definition,[new_symbols(definition,[spl12_24])],[avatar_definition]) ).
fof(f3387,plain,
( sF0 = join(sF0,sF5)
| ~ spl12_24 ),
inference(avatar_component_clause,[],[f3385]) ).
fof(f3388,plain,
( spl12_24
| ~ spl12_1
| ~ spl12_6
| ~ spl12_12
| ~ spl12_16 ),
inference(avatar_split_clause,[],[f1542,f681,f251,f124,f56,f3385]) ).
fof(f4721,definition,
( spl12_27
<=> sF0 = join(sF0,sF10) ),
introduced(definition,[new_symbols(definition,[spl12_27])],[avatar_definition]) ).
fof(f4723,plain,
( sF0 = join(sF0,sF10)
| ~ spl12_27 ),
inference(avatar_component_clause,[],[f4721]) ).
fof(f4724,plain,
( spl12_27
| ~ spl12_8
| ~ spl12_9
| ~ spl12_11
| ~ spl12_13
| ~ spl12_14
| ~ spl12_16 ),
inference(avatar_split_clause,[],[f1547,f681,f671,f257,f245,f169,f154,f4721]) ).
fof(f4975,plain,
( ! [X0] : join(sF11,X0) = join(sF10,join(X0,sF5))
| ~ spl12_3 ),
inference(superposition,[],[f206,f1]) ).
fof(f5238,definition,
( spl12_31
<=> join(sF1,sF2) = join(sF1,sF5) ),
introduced(definition,[new_symbols(definition,[spl12_31])],[avatar_definition]) ).
fof(f5240,plain,
( join(sF1,sF2) = join(sF1,sF5)
| ~ spl12_31 ),
inference(avatar_component_clause,[],[f5238]) ).
fof(f5241,plain,
( spl12_31
| ~ spl12_1
| ~ spl12_7
| ~ spl12_12
| ~ spl12_16 ),
inference(avatar_split_clause,[],[f1631,f681,f251,f139,f56,f5238]) ).
fof(f5297,definition,
( spl12_32
<=> sF2 = join(sF2,sF10) ),
introduced(definition,[new_symbols(definition,[spl12_32])],[avatar_definition]) ).
fof(f5299,plain,
( sF2 = join(sF2,sF10)
| ~ spl12_32 ),
inference(avatar_component_clause,[],[f5297]) ).
fof(f5300,plain,
( spl12_32
| ~ spl12_8
| ~ spl12_10
| ~ spl12_11
| ~ spl12_13
| ~ spl12_14
| ~ spl12_15
| ~ spl12_16 ),
inference(avatar_split_clause,[],[f1829,f681,f676,f671,f257,f245,f188,f154,f5297]) ).
fof(f7278,plain,
( join(sF10,sF0) = join(sF11,sF0)
| ~ spl12_3
| ~ spl12_24 ),
inference(superposition,[],[f4975,f3387]) ).
fof(f7279,plain,
( join(sF11,sF1) = join(sF10,join(sF1,sF2))
| ~ spl12_3
| ~ spl12_31 ),
inference(superposition,[],[f4975,f5240]) ).
fof(f7318,plain,
( join(sF11,sF1) = join(sF2,join(sF10,sF1))
| ~ spl12_3
| ~ spl12_31 ),
inference(forward_demodulation,[],[f7279,f210]) ).
fof(f7319,plain,
( join(sF10,sF0) = join(sF0,sF11)
| ~ spl12_3
| ~ spl12_24 ),
inference(forward_demodulation,[],[f7278,f1]) ).
fof(f7334,plain,
( join(sF11,sF1) = join(sF1,join(sF2,sF10))
| ~ spl12_3
| ~ spl12_31 ),
inference(forward_demodulation,[],[f7318,f210]) ).
fof(f7335,plain,
( join(sF0,sF10) = join(sF0,sF11)
| ~ spl12_3
| ~ spl12_24 ),
inference(forward_demodulation,[],[f7319,f1]) ).
fof(f7344,plain,
( join(sF1,sF2) = join(sF11,sF1)
| ~ spl12_3
| ~ spl12_31
| ~ spl12_32 ),
inference(forward_demodulation,[],[f7334,f5299]) ).
fof(f7345,plain,
( sF0 = join(sF0,sF11)
| ~ spl12_3
| ~ spl12_24
| ~ spl12_27 ),
inference(forward_demodulation,[],[f7335,f4723]) ).
fof(f7346,plain,
( join(sF1,sF2) = join(sF1,sF11)
| ~ spl12_3
| ~ spl12_31
| ~ spl12_32 ),
inference(forward_demodulation,[],[f7344,f1]) ).
fof(f10312,definition,
( spl12_46
<=> join(sF1,sF2) = join(sF1,sF11) ),
introduced(definition,[new_symbols(definition,[spl12_46])],[avatar_definition]) ).
fof(f10314,plain,
( join(sF1,sF2) = join(sF1,sF11)
| ~ spl12_46 ),
inference(avatar_component_clause,[],[f10312]) ).
fof(f10315,plain,
( spl12_46
| ~ spl12_3
| ~ spl12_31
| ~ spl12_32 ),
inference(avatar_split_clause,[],[f7346,f5297,f5238,f89,f10312]) ).
fof(f10321,plain,
( complement(sF11) = join(complement(join(sF1,sF2)),complement(join(sF11,complement(sF1))))
| ~ spl12_46 ),
inference(superposition,[],[f489,f10314]) ).
fof(f10342,plain,
( complement(sF11) = join(complement(join(sF1,sF2)),complement(join(sF11,sF0)))
| ~ spl12_19
| ~ spl12_46 ),
inference(forward_demodulation,[],[f10321,f2080]) ).
fof(f10352,plain,
( complement(sF11) = join(complement(join(sF1,sF2)),complement(join(sF0,sF11)))
| ~ spl12_19
| ~ spl12_46 ),
inference(forward_demodulation,[],[f10342,f1]) ).
fof(f10358,plain,
( complement(sF11) = join(complement(join(sF0,sF11)),complement(join(sF1,sF2)))
| ~ spl12_19
| ~ spl12_46 ),
inference(forward_demodulation,[],[f10352,f1]) ).
fof(f10362,plain,
( complement(sF11) = join(complement(sF0),complement(join(sF1,sF2)))
| ~ spl12_3
| ~ spl12_19
| ~ spl12_24
| ~ spl12_27
| ~ spl12_46 ),
inference(forward_demodulation,[],[f10358,f7345]) ).
fof(f10366,plain,
( complement(sF11) = join(sF1,complement(join(sF1,sF2)))
| ~ spl12_3
| ~ spl12_6
| ~ spl12_19
| ~ spl12_24
| ~ spl12_27
| ~ spl12_46 ),
inference(forward_demodulation,[],[f10362,f126]) ).
fof(f10370,plain,
( complement(sF11) = join(sF1,complement(sF2))
| ~ spl12_3
| ~ spl12_6
| ~ spl12_16
| ~ spl12_19
| ~ spl12_24
| ~ spl12_27
| ~ spl12_46 ),
inference(forward_demodulation,[],[f10366,f1443]) ).
fof(f10372,plain,
( join(sF1,sF3) = complement(sF11)
| ~ spl12_3
| ~ spl12_6
| ~ spl12_7
| ~ spl12_16
| ~ spl12_19
| ~ spl12_24
| ~ spl12_27
| ~ spl12_46 ),
inference(forward_demodulation,[],[f10370,f141]) ).
fof(f10374,plain,
( sF4 = complement(sF11)
| ~ spl12_3
| ~ spl12_6
| ~ spl12_7
| ~ spl12_12
| ~ spl12_16
| ~ spl12_19
| ~ spl12_24
| ~ spl12_27
| ~ spl12_46 ),
inference(forward_demodulation,[],[f10372,f253]) ).
fof(f10410,definition,
( spl12_47
<=> sF4 = complement(sF11) ),
introduced(definition,[new_symbols(definition,[spl12_47])],[avatar_definition]) ).
fof(f10412,plain,
( sF4 = complement(sF11)
| ~ spl12_47 ),
inference(avatar_component_clause,[],[f10410]) ).
fof(f10413,plain,
( spl12_47
| ~ spl12_3
| ~ spl12_6
| ~ spl12_7
| ~ spl12_12
| ~ spl12_16
| ~ spl12_19
| ~ spl12_24
| ~ spl12_27
| ~ spl12_46 ),
inference(avatar_split_clause,[],[f10374,f10312,f4721,f3385,f2078,f681,f251,f139,f124,f89,f10410]) ).
fof(f10414,plain,
( ! [X0] : sF11 = join(complement(join(sF4,complement(X0))),complement(join(sF4,X0)))
| ~ spl12_47 ),
inference(superposition,[],[f4,f10412]) ).
fof(f10447,plain,
( ! [X0] : sF11 = join(complement(join(sF4,X0)),complement(join(sF4,complement(X0))))
| ~ spl12_47 ),
inference(forward_demodulation,[],[f10414,f1]) ).
fof(f10450,plain,
( complement(sF4) = sF11
| ~ spl12_47 ),
inference(forward_demodulation,[],[f10447,f479]) ).
fof(f10451,plain,
( sF5 = sF11
| ~ spl12_1
| ~ spl12_47 ),
inference(forward_demodulation,[],[f10450,f58]) ).
fof(f10452,plain,
( $false
| ~ spl12_1
| spl12_2
| ~ spl12_47 ),
inference(forward_subsumption_resolution,[],[f10451,f63]) ).
fof(f10453,plain,
( ~ spl12_1
| spl12_2
| ~ spl12_47 ),
inference(avatar_contradiction_clause,[],[f10452]) ).
cnf(s1,plain,
spl12_1,
inference(sat_conversion,[],[f59]) ).
cnf(s2,plain,
~ spl12_2,
inference(sat_conversion,[],[f64]) ).
cnf(s3,plain,
spl12_3,
inference(sat_conversion,[],[f92]) ).
cnf(s4,plain,
spl12_4,
inference(sat_conversion,[],[f97]) ).
cnf(s5,plain,
spl12_5,
inference(sat_conversion,[],[f106]) ).
cnf(s6,plain,
spl12_6,
inference(sat_conversion,[],[f127]) ).
cnf(s7,plain,
spl12_7,
inference(sat_conversion,[],[f142]) ).
cnf(s8,plain,
spl12_8,
inference(sat_conversion,[],[f157]) ).
cnf(s9,plain,
spl12_9,
inference(sat_conversion,[],[f172]) ).
cnf(s10,plain,
spl12_10,
inference(sat_conversion,[],[f191]) ).
cnf(s11,plain,
spl12_11,
inference(sat_conversion,[],[f248]) ).
cnf(s12,plain,
spl12_12,
inference(sat_conversion,[],[f254]) ).
cnf(s13,plain,
spl12_13,
inference(sat_conversion,[],[f260]) ).
cnf(s14,plain,
( ~ spl12_4
| spl12_14 ),
inference(sat_conversion,[],[f674]) ).
cnf(s15,plain,
( ~ spl12_5
| spl12_15 ),
inference(sat_conversion,[],[f679]) ).
cnf(s16,plain,
spl12_16,
inference(sat_conversion,[],[f684]) ).
cnf(s19,plain,
( ~ spl12_6
| spl12_19 ),
inference(sat_conversion,[],[f2081]) ).
cnf(s24,plain,
( ~ spl12_1
| ~ spl12_6
| ~ spl12_12
| ~ spl12_16
| spl12_24 ),
inference(sat_conversion,[],[f3388]) ).
cnf(s27,plain,
( ~ spl12_8
| ~ spl12_9
| ~ spl12_11
| ~ spl12_13
| ~ spl12_14
| ~ spl12_16
| spl12_27 ),
inference(sat_conversion,[],[f4724]) ).
cnf(s31,plain,
( ~ spl12_1
| ~ spl12_7
| ~ spl12_12
| ~ spl12_16
| spl12_31 ),
inference(sat_conversion,[],[f5241]) ).
cnf(s32,plain,
( ~ spl12_8
| ~ spl12_10
| ~ spl12_11
| ~ spl12_13
| ~ spl12_14
| ~ spl12_15
| ~ spl12_16
| spl12_32 ),
inference(sat_conversion,[],[f5300]) ).
cnf(s46,plain,
( ~ spl12_3
| ~ spl12_31
| ~ spl12_32
| spl12_46 ),
inference(sat_conversion,[],[f10315]) ).
cnf(s47,plain,
( ~ spl12_3
| ~ spl12_6
| ~ spl12_7
| ~ spl12_12
| ~ spl12_16
| ~ spl12_19
| ~ spl12_24
| ~ spl12_27
| ~ spl12_46
| spl12_47 ),
inference(sat_conversion,[],[f10413]) ).
cnf(s49,plain,
( ~ spl12_1
| spl12_2
| ~ spl12_47 ),
inference(sat_conversion,[],[f10453]) ).
cnf(s58,plain,
spl12_19,
inference(rat,[],[s19,s6]) ).
cnf(s61,plain,
spl12_15,
inference(rat,[],[s15,s5]) ).
cnf(s66,plain,
spl12_14,
inference(rat,[],[s14,s4]) ).
cnf(s70,plain,
spl12_32,
inference(rat,[],[s32,s61,s16,s8,s10,s13,s11,s66]) ).
cnf(s71,plain,
spl12_27,
inference(rat,[],[s27,s8,s16,s9,s13,s11,s66]) ).
cnf(s74,plain,
~ spl12_47,
inference(rat,[],[s49,s2,s1]) ).
cnf(s78,plain,
spl12_31,
inference(rat,[],[s31,s7,s16,s12,s1]) ).
cnf(s79,plain,
spl12_24,
inference(rat,[],[s24,s6,s16,s12,s1]) ).
cnf(s81,plain,
spl12_46,
inference(rat,[],[s46,s3,s70,s78]) ).
cnf(s82,plain,
$false,
inference(rat,[],[s47,s74,s3,s71,s58,s6,s16,s12,s7,s81,s79]) ).
fof(f10454,plain,
$false,
inference(avatar_sat_refutation,[],[s82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL032-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:54:24 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.26/3.38 % (3421567)Detected a unit-equality problem, will run specialized UEQ schedule.
% 15.26/3.38 % (3421701)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2049528107:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 15.26/3.38 % (3421699)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=713904533:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 15.26/3.38 % (3421698)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=844807796:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 15.26/3.38 % (3421700)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2422039783:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 15.26/3.38 % (3421701)Instruction limit reached!
% 15.26/3.38 % (3421701)------------------------------
% 15.26/3.38 % (3421701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.26/3.38 % (3421701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.26/3.38 % (3421701)CaDiCaL version: 2.1.3
% 15.26/3.38 % (3421701)Termination reason: Instruction limit
% 15.26/3.38 % (3421701)Termination phase: Saturation
% 15.26/3.38 % (3421701)Time elapsed: 0.047 s
% 15.26/3.38 % (3421701)Peak memory usage: 89 MB
% 15.26/3.38 % (3421701)Instructions burned: 137 (million)
% 15.26/3.38 % (3421704)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3685007423:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 15.26/3.38 % (3421702)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=541180966:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 15.26/3.38 % (3421703)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2590304432:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 15.26/3.38 % (3421709)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1036600509:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 15.26/3.38 % (3421702)Instruction limit reached!
% 15.26/3.38 % (3421702)------------------------------
% 15.26/3.38 % (3421702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.26/3.38 % (3421702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.26/3.38 % (3421702)CaDiCaL version: 2.1.3
% 15.26/3.38 % (3421702)Termination reason: Instruction limit
% 15.26/3.38 % (3421702)Termination phase: Saturation
% 15.26/3.38 % (3421702)Time elapsed: 0.105 s
% 15.26/3.38 % (3421702)Peak memory usage: 89 MB
% 15.26/3.38 % (3421702)Instructions burned: 181 (million)
% 15.26/3.38 % (3421703)Instruction limit reached!
% 15.26/3.38 % (3421703)------------------------------
% 15.26/3.38 % (3421703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.26/3.38 % (3421703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.26/3.38 % (3421703)CaDiCaL version: 2.1.3
% 15.26/3.38 % (3421703)Termination reason: Instruction limit
% 15.26/3.38 % (3421703)Termination phase: Saturation
% 15.26/3.38 % (3421703)Time elapsed: 0.173 s
% 15.26/3.38 % (3421703)Peak memory usage: 90 MB
% 15.26/3.38 % (3421703)Instructions burned: 258 (million)
% 15.26/3.38 % (3421714)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1275455812:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 15.26/3.38 % (3421722)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=817520750:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 15.26/3.38 % (3421722)Instruction limit reached!
% 15.26/3.38 % (3421722)------------------------------
% 15.26/3.38 % (3421722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.26/3.38 % (3421722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.26/3.38 % (3421722)CaDiCaL version: 2.1.3
% 15.26/3.38 % (3421722)Termination reason: Instruction limit
% 15.26/3.38 % (3421722)Termination phase: Saturation
% 15.26/3.38 % (3421722)Time elapsed: 0.130 s
% 15.26/3.38 % (3421722)Peak memory usage: 89 MB
% 15.26/3.38 % (3421722)Instructions burned: 215 (million)
% 15.26/3.38 % (3421809)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=3116971047:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 15.26/3.38 % (3421704)Instruction limit reached!
% 15.26/3.38 % (3421704)------------------------------
% 15.26/3.38 % (3421704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.26/3.38 % (3421704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.26/3.38 % (3421704)CaDiCaL version: 2.1.3
% 15.26/3.38 % (3421704)Termination reason: Instruction limit
% 15.26/3.38 % (3421704)Termination phase: Saturation
% 15.26/3.38 % (3421704)Time elapsed: 0.666 s
% 15.26/3.38 % (3421704)Peak memory usage: 98 MB
% 15.26/3.38 % (3421704)Instructions burned: 1187 (million)
% 15.26/3.38 % (3421809)Instruction limit reached!
% 15.26/3.38 % (3421809)------------------------------
% 15.26/3.38 % (3421809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.26/3.38 % (3421809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.26/3.38 % (3421809)CaDiCaL version: 2.1.3
% 15.26/3.38 % (3421809)Termination reason: Instruction limit
% 15.26/3.38 % (3421809)Termination phase: Saturation
% 15.26/3.38 % (3421809)Time elapsed: 0.195 s
% 15.26/3.38 % (3421809)Peak memory usage: 92 MB
% 15.26/3.38 % (3421809)Instructions burned: 317 (million)
% 15.26/3.38 % (3421821)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=3068940884:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 15.26/3.38 % (3421709)Instruction limit reached!
% 15.26/3.38 % (3421709)------------------------------
% 15.26/3.38 % (3421709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.26/3.38 % (3421709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.26/3.38 % (3421709)CaDiCaL version: 2.1.3
% 15.26/3.38 % (3421709)Termination reason: Instruction limit
% 15.26/3.38 % (3421709)Termination phase: Saturation
% 15.26/3.38 % (3421709)Time elapsed: 0.902 s
% 15.26/3.38 % (3421709)Peak memory usage: 141 MB
% 15.26/3.38 % (3421709)Instructions burned: 2051 (million)
% 15.26/3.38 % (3421844)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=217361954:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 15.26/3.38 % (3421859)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=592487558:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2988 on theBenchmark for (2988ds/14534Mi)
% 15.26/3.38 % (3421698)First to succeed.
% 15.26/3.38 % (3421698)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3421567"
% 15.26/3.38 % (3421700)Also succeeded, but the first one will report.
% 15.26/3.38 % (3421821)Also succeeded, but the first one will report.
% 15.26/3.38 % (3421698)Refutation found. Thanks to Tanya!
% 15.26/3.38 % SZS status Unsatisfiable for theBenchmark
% 15.26/3.38 % SZS output start Proof for theBenchmark
% See solution above
% 18.26/3.56 % (3421698)------------------------------
% 18.26/3.56 % (3421698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.26/3.56 % (3421698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.26/3.56 % (3421698)CaDiCaL version: 2.1.3
% 18.26/3.56 % (3421698)Termination reason: Refutation
% 18.26/3.56 % (3421698)Time elapsed: 1.926 s
% 18.26/3.56 % (3421698)Peak memory usage: 145 MB
% 18.26/3.56 % (3421698)Instructions burned: 2363 (million)
% 18.26/3.56 % (3421698)------------------------------
% 18.26/3.56 % (3421698)------------------------------
% 18.26/3.56 % (3421567)Success in time 2.525 s
% 18.26/3.56 % Vampire exiting
%------------------------------------------------------------------------------