TSTP Solution File: GRP190-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP190-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 15:39:31 EDT 2023
% Result : Unsatisfiable 36.66s 5.68s
% Output : Refutation 36.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 40
% Syntax : Number of formulae : 292 ( 95 unt; 0 def)
% Number of atoms : 490 ( 228 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 374 ( 176 ~; 175 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 170 (; 170 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f78641,plain,
$false,
inference(avatar_smt_refutation,[],[f22,f27,f60,f71,f72,f73,f74,f122,f123,f886,f945,f946,f10761,f10800,f10801,f10802,f10803,f10998,f11050,f11051,f11052,f11053,f11054,f11055,f11112,f11117,f11213,f11214,f11215,f11216,f11217,f11218,f13661,f13662,f13663,f13664,f13725,f13726,f30813,f30899,f30900,f30901,f30902,f30903,f30904,f30905,f31626,f31728,f31733,f34448,f34543,f34544,f34545,f34546,f34547,f34548,f34549,f34550,f34655,f34660,f78512,f78599]) ).
fof(f78599,plain,
( spl0_2
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f78598]) ).
fof(f78598,plain,
( $false
| spl0_2
| ~ spl0_23 ),
inference(subsumption_resolution,[],[f78541,f26]) ).
fof(f26,plain,
( inverse(b) != least_upper_bound(inverse(a),inverse(b))
| spl0_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f24,plain,
( spl0_2
<=> inverse(b) = least_upper_bound(inverse(a),inverse(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f78541,plain,
( inverse(b) = least_upper_bound(inverse(a),inverse(b))
| ~ spl0_23 ),
inference(superposition,[],[f849,f78511]) ).
fof(f78511,plain,
( inverse(a) = greatest_lower_bound(inverse(a),inverse(b))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f78509]) ).
fof(f78509,plain,
( spl0_23
<=> inverse(a) = greatest_lower_bound(inverse(a),inverse(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f849,plain,
! [X8,X7] : least_upper_bound(greatest_lower_bound(X8,X7),X7) = X7,
inference(superposition,[],[f252,f29]) ).
fof(f29,plain,
! [X2,X1] : least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(superposition,[],[f10,f4]) ).
fof(f4,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',symmetry_of_glb) ).
fof(f10,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',lub_absorbtion) ).
fof(f252,plain,
! [X4,X5] : least_upper_bound(X5,X4) = least_upper_bound(X4,least_upper_bound(X5,X4)),
inference(superposition,[],[f189,f5]) ).
fof(f5,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',symmetry_of_lub) ).
fof(f189,plain,
! [X2,X1] : least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X1,X2)),
inference(superposition,[],[f7,f8]) ).
fof(f8,axiom,
! [X0] : least_upper_bound(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',idempotence_of_lub) ).
fof(f7,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',associativity_of_lub) ).
fof(f78512,plain,
( spl0_23
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f78392,f34540,f78509]) ).
fof(f34540,plain,
( spl0_20
<=> identity = least_upper_bound(multiply(b,inverse(a)),identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f78392,plain,
( inverse(a) = greatest_lower_bound(inverse(a),inverse(b))
| ~ spl0_20 ),
inference(forward_demodulation,[],[f78112,f336]) ).
fof(f336,plain,
! [X5] : multiply(X5,identity) = X5,
inference(superposition,[],[f80,f78]) ).
fof(f78,plain,
! [X1] : multiply(inverse(inverse(X1)),identity) = X1,
inference(superposition,[],[f45,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',left_inverse) ).
fof(f45,plain,
! [X2,X3] : multiply(inverse(X2),multiply(X2,X3)) = X3,
inference(forward_demodulation,[],[f43,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',left_identity) ).
fof(f43,plain,
! [X2,X3] : multiply(inverse(X2),multiply(X2,X3)) = multiply(identity,X3),
inference(superposition,[],[f3,f2]) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',associativity) ).
fof(f80,plain,
! [X6,X5] : multiply(X5,X6) = multiply(inverse(inverse(X5)),X6),
inference(superposition,[],[f45,f45]) ).
fof(f78112,plain,
( inverse(a) = greatest_lower_bound(inverse(a),multiply(inverse(b),identity))
| ~ spl0_20 ),
inference(superposition,[],[f11240,f34542]) ).
fof(f34542,plain,
( identity = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f34540]) ).
fof(f11240,plain,
! [X50,X51,X49] : greatest_lower_bound(X50,multiply(inverse(X49),least_upper_bound(multiply(X49,X50),X51))) = X50,
inference(superposition,[],[f372,f45]) ).
fof(f372,plain,
! [X14,X12,X13] : multiply(X12,X13) = greatest_lower_bound(multiply(X12,X13),multiply(X12,least_upper_bound(X13,X14))),
inference(superposition,[],[f11,f12]) ).
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',monotony_lub1) ).
fof(f11,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',glb_absorbtion) ).
fof(f34660,plain,
( spl0_22
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f34530,f34445,f34657]) ).
fof(f34657,plain,
( spl0_22
<=> identity = greatest_lower_bound(inverse(multiply(b,inverse(a))),identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f34445,plain,
( spl0_19
<=> identity = least_upper_bound(identity,multiply(b,inverse(a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f34530,plain,
( identity = greatest_lower_bound(inverse(multiply(b,inverse(a))),identity)
| ~ spl0_19 ),
inference(forward_demodulation,[],[f34499,f336]) ).
fof(f34499,plain,
( identity = greatest_lower_bound(multiply(inverse(multiply(b,inverse(a))),identity),identity)
| ~ spl0_19 ),
inference(superposition,[],[f14068,f34447]) ).
fof(f34447,plain,
( identity = least_upper_bound(identity,multiply(b,inverse(a)))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f34445]) ).
fof(f14068,plain,
! [X56,X55] : identity = greatest_lower_bound(multiply(inverse(X55),least_upper_bound(X56,X55)),identity),
inference(superposition,[],[f138,f9203]) ).
fof(f9203,plain,
! [X21,X20] : identity = greatest_lower_bound(identity,multiply(inverse(X20),least_upper_bound(X21,X20))),
inference(superposition,[],[f33,f357]) ).
fof(f357,plain,
! [X2,X3] : multiply(inverse(X2),least_upper_bound(X3,X2)) = least_upper_bound(multiply(inverse(X2),X3),identity),
inference(superposition,[],[f12,f2]) ).
fof(f33,plain,
! [X2,X1] : greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f138,plain,
! [X2,X1] : greatest_lower_bound(X2,X1) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)),
inference(superposition,[],[f83,f4]) ).
fof(f83,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1)),
inference(superposition,[],[f6,f9]) ).
fof(f9,axiom,
! [X0] : greatest_lower_bound(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',idempotence_of_gld) ).
fof(f6,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',associativity_of_glb) ).
fof(f34655,plain,
( spl0_21
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f34524,f34445,f34652]) ).
fof(f34652,plain,
( spl0_21
<=> identity = greatest_lower_bound(identity,inverse(multiply(b,inverse(a)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f34524,plain,
( identity = greatest_lower_bound(identity,inverse(multiply(b,inverse(a))))
| ~ spl0_19 ),
inference(forward_demodulation,[],[f34493,f336]) ).
fof(f34493,plain,
( identity = greatest_lower_bound(identity,multiply(inverse(multiply(b,inverse(a))),identity))
| ~ spl0_19 ),
inference(superposition,[],[f9203,f34447]) ).
fof(f34550,plain,
( spl0_20
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f34531,f34445,f34540]) ).
fof(f34531,plain,
( identity = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(forward_demodulation,[],[f34500,f1]) ).
fof(f34500,plain,
( multiply(identity,identity) = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(superposition,[],[f15021,f34447]) ).
fof(f15021,plain,
! [X40,X39] : least_upper_bound(X39,X40) = multiply(least_upper_bound(X40,X39),identity),
inference(forward_demodulation,[],[f15020,f400]) ).
fof(f400,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f336,f78]) ).
fof(f15020,plain,
! [X40,X39] : least_upper_bound(X39,X40) = multiply(least_upper_bound(X40,inverse(inverse(X39))),identity),
inference(forward_demodulation,[],[f14924,f336]) ).
fof(f14924,plain,
! [X40,X39] : multiply(least_upper_bound(X40,inverse(inverse(X39))),identity) = least_upper_bound(X39,multiply(X40,identity)),
inference(superposition,[],[f747,f78]) ).
fof(f747,plain,
! [X8,X9,X7] : least_upper_bound(multiply(X9,X8),multiply(X7,X8)) = multiply(least_upper_bound(X7,X9),X8),
inference(superposition,[],[f14,f5]) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',monotony_lub2) ).
fof(f34549,plain,
( spl0_20
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f34528,f34445,f34540]) ).
fof(f34528,plain,
( identity = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(forward_demodulation,[],[f34497,f8]) ).
fof(f34497,plain,
( least_upper_bound(identity,identity) = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(superposition,[],[f9705,f34447]) ).
fof(f9705,plain,
! [X21,X22] : least_upper_bound(X22,X21) = least_upper_bound(least_upper_bound(X21,X22),X21),
inference(forward_demodulation,[],[f9621,f1]) ).
fof(f9621,plain,
! [X21,X22] : least_upper_bound(least_upper_bound(X21,X22),X21) = multiply(identity,least_upper_bound(X22,X21)),
inference(superposition,[],[f9560,f3751]) ).
fof(f3751,plain,
! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(X0,least_upper_bound(X0,X1)),
inference(superposition,[],[f198,f8]) ).
fof(f198,plain,
! [X8,X9,X7] : least_upper_bound(X9,least_upper_bound(X7,X8)) = least_upper_bound(X7,least_upper_bound(X8,X9)),
inference(superposition,[],[f7,f5]) ).
fof(f9560,plain,
! [X0,X1] : least_upper_bound(X1,X0) = multiply(identity,least_upper_bound(X0,X1)),
inference(forward_demodulation,[],[f9476,f1]) ).
fof(f9476,plain,
! [X0,X1] : multiply(identity,least_upper_bound(X0,X1)) = least_upper_bound(multiply(identity,X1),X0),
inference(superposition,[],[f366,f1]) ).
fof(f366,plain,
! [X6,X7,X5] : least_upper_bound(multiply(X5,X7),multiply(X5,X6)) = multiply(X5,least_upper_bound(X6,X7)),
inference(superposition,[],[f12,f5]) ).
fof(f34548,plain,
( spl0_20
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f34527,f34445,f34540]) ).
fof(f34527,plain,
( identity = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(forward_demodulation,[],[f34496,f1]) ).
fof(f34496,plain,
( multiply(identity,identity) = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(superposition,[],[f9560,f34447]) ).
fof(f34547,plain,
( spl0_20
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f34526,f34445,f34540]) ).
fof(f34526,plain,
( identity = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(forward_demodulation,[],[f34495,f77]) ).
fof(f77,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(superposition,[],[f45,f1]) ).
fof(f34495,plain,
( identity = least_upper_bound(multiply(inverse(identity),multiply(b,inverse(a))),identity)
| ~ spl0_19 ),
inference(superposition,[],[f9228,f34447]) ).
fof(f9228,plain,
! [X28,X27] : identity = least_upper_bound(multiply(inverse(least_upper_bound(X28,X27)),X27),identity),
inference(forward_demodulation,[],[f9122,f2]) ).
fof(f9122,plain,
! [X28,X27] : least_upper_bound(multiply(inverse(least_upper_bound(X28,X27)),X27),identity) = multiply(inverse(least_upper_bound(X28,X27)),least_upper_bound(X28,X27)),
inference(superposition,[],[f357,f252]) ).
fof(f34546,plain,
( spl0_20
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f34520,f34445,f34540]) ).
fof(f34520,plain,
( identity = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(forward_demodulation,[],[f34488,f8]) ).
fof(f34488,plain,
( least_upper_bound(identity,identity) = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(superposition,[],[f3751,f34447]) ).
fof(f34545,plain,
( spl0_20
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f34512,f34445,f34540]) ).
fof(f34512,plain,
( identity = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(forward_demodulation,[],[f34455,f8]) ).
fof(f34455,plain,
( least_upper_bound(identity,identity) = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(superposition,[],[f5518,f34447]) ).
fof(f5518,plain,
! [X9] : least_upper_bound(X9,identity) = least_upper_bound(least_upper_bound(identity,X9),identity),
inference(forward_demodulation,[],[f5488,f336]) ).
fof(f5488,plain,
! [X9] : least_upper_bound(least_upper_bound(identity,X9),identity) = multiply(least_upper_bound(X9,identity),identity),
inference(superposition,[],[f5460,f3751]) ).
fof(f5460,plain,
! [X10] : least_upper_bound(X10,identity) = multiply(least_upper_bound(identity,X10),identity),
inference(forward_demodulation,[],[f5459,f400]) ).
fof(f5459,plain,
! [X10] : multiply(least_upper_bound(identity,inverse(inverse(X10))),identity) = least_upper_bound(X10,identity),
inference(forward_demodulation,[],[f5386,f5]) ).
fof(f5386,plain,
! [X10] : least_upper_bound(X10,identity) = multiply(least_upper_bound(inverse(inverse(X10)),identity),identity),
inference(superposition,[],[f733,f78]) ).
fof(f733,plain,
! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0),
inference(superposition,[],[f14,f1]) ).
fof(f34544,plain,
( spl0_20
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f34509,f34445,f34540]) ).
fof(f34509,plain,
( identity = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(forward_demodulation,[],[f34453,f1]) ).
fof(f34453,plain,
( multiply(identity,identity) = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(superposition,[],[f5460,f34447]) ).
fof(f34543,plain,
( spl0_20
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f34477,f34445,f34540]) ).
fof(f34477,plain,
( identity = least_upper_bound(multiply(b,inverse(a)),identity)
| ~ spl0_19 ),
inference(superposition,[],[f252,f34447]) ).
fof(f34448,plain,
( spl0_19
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f34215,f68,f34445]) ).
fof(f68,plain,
( spl0_4
<=> b = greatest_lower_bound(a,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f34215,plain,
( identity = least_upper_bound(identity,multiply(b,inverse(a)))
| ~ spl0_4 ),
inference(superposition,[],[f17747,f70]) ).
fof(f70,plain,
( b = greatest_lower_bound(a,b)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f17747,plain,
! [X62,X61] : identity = least_upper_bound(identity,multiply(greatest_lower_bound(X61,X62),inverse(X61))),
inference(superposition,[],[f920,f335]) ).
fof(f335,plain,
! [X2] : identity = multiply(X2,inverse(X2)),
inference(superposition,[],[f80,f2]) ).
fof(f920,plain,
! [X16,X14,X15] : multiply(X14,X15) = least_upper_bound(multiply(X14,X15),multiply(greatest_lower_bound(X14,X16),X15)),
inference(superposition,[],[f10,f15]) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',monotony_glb2) ).
fof(f31733,plain,
( spl0_18
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f30893,f30810,f31730]) ).
fof(f31730,plain,
( spl0_18
<=> identity = least_upper_bound(inverse(multiply(a,inverse(b))),identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f30810,plain,
( spl0_15
<=> identity = greatest_lower_bound(identity,multiply(a,inverse(b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f30893,plain,
( identity = least_upper_bound(inverse(multiply(a,inverse(b))),identity)
| ~ spl0_15 ),
inference(forward_demodulation,[],[f30865,f336]) ).
fof(f30865,plain,
( identity = least_upper_bound(multiply(inverse(multiply(a,inverse(b))),identity),identity)
| ~ spl0_15 ),
inference(superposition,[],[f13899,f30812]) ).
fof(f30812,plain,
( identity = greatest_lower_bound(identity,multiply(a,inverse(b)))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f30810]) ).
fof(f13899,plain,
! [X70,X71] : identity = least_upper_bound(multiply(inverse(X70),greatest_lower_bound(X71,X70)),identity),
inference(superposition,[],[f252,f9069]) ).
fof(f9069,plain,
! [X14,X13] : identity = least_upper_bound(identity,multiply(inverse(X13),greatest_lower_bound(X14,X13))),
inference(forward_demodulation,[],[f8965,f2]) ).
fof(f8965,plain,
! [X14,X13] : multiply(inverse(X13),X13) = least_upper_bound(identity,multiply(inverse(X13),greatest_lower_bound(X14,X13))),
inference(superposition,[],[f348,f29]) ).
fof(f348,plain,
! [X2,X3] : multiply(inverse(X2),least_upper_bound(X2,X3)) = least_upper_bound(identity,multiply(inverse(X2),X3)),
inference(superposition,[],[f12,f2]) ).
fof(f31728,plain,
( spl0_17
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f30885,f30810,f31725]) ).
fof(f31725,plain,
( spl0_17
<=> identity = least_upper_bound(identity,inverse(multiply(a,inverse(b)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f30885,plain,
( identity = least_upper_bound(identity,inverse(multiply(a,inverse(b))))
| ~ spl0_15 ),
inference(forward_demodulation,[],[f30856,f336]) ).
fof(f30856,plain,
( identity = least_upper_bound(identity,multiply(inverse(multiply(a,inverse(b))),identity))
| ~ spl0_15 ),
inference(superposition,[],[f9069,f30812]) ).
fof(f31626,plain,
( spl0_16
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f30894,f30810,f30896]) ).
fof(f30896,plain,
( spl0_16
<=> identity = greatest_lower_bound(multiply(a,inverse(b)),identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f30894,plain,
( identity = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(forward_demodulation,[],[f30866,f1]) ).
fof(f30866,plain,
( multiply(identity,identity) = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(superposition,[],[f16787,f30812]) ).
fof(f16787,plain,
! [X40,X39] : greatest_lower_bound(X39,X40) = multiply(greatest_lower_bound(X40,X39),identity),
inference(forward_demodulation,[],[f16786,f400]) ).
fof(f16786,plain,
! [X40,X39] : greatest_lower_bound(X39,X40) = multiply(greatest_lower_bound(X40,inverse(inverse(X39))),identity),
inference(forward_demodulation,[],[f16680,f336]) ).
fof(f16680,plain,
! [X40,X39] : multiply(greatest_lower_bound(X40,inverse(inverse(X39))),identity) = greatest_lower_bound(X39,multiply(X40,identity)),
inference(superposition,[],[f913,f78]) ).
fof(f913,plain,
! [X8,X9,X7] : greatest_lower_bound(multiply(X9,X8),multiply(X7,X8)) = multiply(greatest_lower_bound(X7,X9),X8),
inference(superposition,[],[f15,f4]) ).
fof(f30905,plain,
( spl0_16
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f30892,f30810,f30896]) ).
fof(f30892,plain,
( identity = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(forward_demodulation,[],[f30863,f9]) ).
fof(f30863,plain,
( greatest_lower_bound(identity,identity) = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(superposition,[],[f12882,f30812]) ).
fof(f12882,plain,
! [X16,X15] : greatest_lower_bound(X16,X15) = greatest_lower_bound(greatest_lower_bound(X15,X16),X15),
inference(forward_demodulation,[],[f12779,f1]) ).
fof(f12779,plain,
! [X16,X15] : greatest_lower_bound(greatest_lower_bound(X15,X16),X15) = multiply(identity,greatest_lower_bound(X16,X15)),
inference(superposition,[],[f12733,f1799]) ).
fof(f1799,plain,
! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1)),
inference(superposition,[],[f92,f9]) ).
fof(f92,plain,
! [X6,X7,X5] : greatest_lower_bound(X5,greatest_lower_bound(X6,X7)) = greatest_lower_bound(X7,greatest_lower_bound(X5,X6)),
inference(superposition,[],[f6,f4]) ).
fof(f12733,plain,
! [X0,X1] : greatest_lower_bound(X1,X0) = multiply(identity,greatest_lower_bound(X0,X1)),
inference(forward_demodulation,[],[f12637,f1]) ).
fof(f12637,plain,
! [X0,X1] : multiply(identity,greatest_lower_bound(X0,X1)) = greatest_lower_bound(multiply(identity,X1),X0),
inference(superposition,[],[f513,f1]) ).
fof(f513,plain,
! [X6,X7,X5] : greatest_lower_bound(multiply(X5,X7),multiply(X5,X6)) = multiply(X5,greatest_lower_bound(X6,X7)),
inference(superposition,[],[f13,f4]) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',monotony_glb1) ).
fof(f30904,plain,
( spl0_16
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f30891,f30810,f30896]) ).
fof(f30891,plain,
( identity = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(forward_demodulation,[],[f30862,f1]) ).
fof(f30862,plain,
( multiply(identity,identity) = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(superposition,[],[f12733,f30812]) ).
fof(f30903,plain,
( spl0_16
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f30890,f30810,f30896]) ).
fof(f30890,plain,
( identity = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(forward_demodulation,[],[f30861,f77]) ).
fof(f30861,plain,
( identity = greatest_lower_bound(multiply(inverse(identity),multiply(a,inverse(b))),identity)
| ~ spl0_15 ),
inference(superposition,[],[f12380,f30812]) ).
fof(f12380,plain,
! [X21,X22] : identity = greatest_lower_bound(multiply(inverse(greatest_lower_bound(X22,X21)),X21),identity),
inference(forward_demodulation,[],[f12253,f2]) ).
fof(f12253,plain,
! [X21,X22] : greatest_lower_bound(multiply(inverse(greatest_lower_bound(X22,X21)),X21),identity) = multiply(inverse(greatest_lower_bound(X22,X21)),greatest_lower_bound(X22,X21)),
inference(superposition,[],[f501,f138]) ).
fof(f501,plain,
! [X2,X3] : multiply(inverse(X2),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(inverse(X2),X3),identity),
inference(superposition,[],[f13,f2]) ).
fof(f30902,plain,
( spl0_16
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f30883,f30810,f30896]) ).
fof(f30883,plain,
( identity = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(forward_demodulation,[],[f30854,f9]) ).
fof(f30854,plain,
( greatest_lower_bound(identity,identity) = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(superposition,[],[f1799,f30812]) ).
fof(f30901,plain,
( spl0_16
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f30874,f30810,f30896]) ).
fof(f30874,plain,
( identity = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(forward_demodulation,[],[f30820,f9]) ).
fof(f30820,plain,
( greatest_lower_bound(identity,identity) = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(superposition,[],[f6352,f30812]) ).
fof(f6352,plain,
! [X5] : greatest_lower_bound(X5,identity) = greatest_lower_bound(greatest_lower_bound(identity,X5),identity),
inference(forward_demodulation,[],[f6318,f336]) ).
fof(f6318,plain,
! [X5] : greatest_lower_bound(greatest_lower_bound(identity,X5),identity) = multiply(greatest_lower_bound(X5,identity),identity),
inference(superposition,[],[f6232,f1799]) ).
fof(f6232,plain,
! [X10] : greatest_lower_bound(X10,identity) = multiply(greatest_lower_bound(identity,X10),identity),
inference(forward_demodulation,[],[f6231,f400]) ).
fof(f6231,plain,
! [X10] : greatest_lower_bound(X10,identity) = multiply(greatest_lower_bound(identity,inverse(inverse(X10))),identity),
inference(forward_demodulation,[],[f6157,f4]) ).
fof(f6157,plain,
! [X10] : greatest_lower_bound(X10,identity) = multiply(greatest_lower_bound(inverse(inverse(X10)),identity),identity),
inference(superposition,[],[f899,f78]) ).
fof(f899,plain,
! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0),
inference(superposition,[],[f15,f1]) ).
fof(f30900,plain,
( spl0_16
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f30871,f30810,f30896]) ).
fof(f30871,plain,
( identity = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(forward_demodulation,[],[f30818,f1]) ).
fof(f30818,plain,
( multiply(identity,identity) = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(superposition,[],[f6232,f30812]) ).
fof(f30899,plain,
( spl0_16
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f30841,f30810,f30896]) ).
fof(f30841,plain,
( identity = greatest_lower_bound(multiply(a,inverse(b)),identity)
| ~ spl0_15 ),
inference(superposition,[],[f138,f30812]) ).
fof(f30813,plain,
( spl0_15
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f30614,f883,f30810]) ).
fof(f883,plain,
( spl0_6
<=> a = least_upper_bound(b,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f30614,plain,
( identity = greatest_lower_bound(identity,multiply(a,inverse(b)))
| ~ spl0_6 ),
inference(superposition,[],[f16275,f885]) ).
fof(f885,plain,
( a = least_upper_bound(b,a)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f883]) ).
fof(f16275,plain,
! [X58,X59] : identity = greatest_lower_bound(identity,multiply(least_upper_bound(X58,X59),inverse(X58))),
inference(superposition,[],[f754,f335]) ).
fof(f754,plain,
! [X16,X14,X15] : multiply(X14,X15) = greatest_lower_bound(multiply(X14,X15),multiply(least_upper_bound(X14,X16),X15)),
inference(superposition,[],[f11,f14]) ).
fof(f13726,plain,
( spl0_14
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f13138,f11114,f13658]) ).
fof(f13658,plain,
( spl0_14
<=> identity = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f11114,plain,
( spl0_12
<=> identity = greatest_lower_bound(identity,inverse(multiply(inverse(a),b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f13138,plain,
( identity = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity)
| ~ spl0_12 ),
inference(forward_demodulation,[],[f12999,f9]) ).
fof(f12999,plain,
( greatest_lower_bound(identity,identity) = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity)
| ~ spl0_12 ),
inference(superposition,[],[f12882,f11116]) ).
fof(f11116,plain,
( identity = greatest_lower_bound(identity,inverse(multiply(inverse(a),b)))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f11114]) ).
fof(f13725,plain,
( spl0_14
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f12897,f11114,f13658]) ).
fof(f12897,plain,
( identity = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity)
| ~ spl0_12 ),
inference(forward_demodulation,[],[f12794,f1]) ).
fof(f12794,plain,
( multiply(identity,identity) = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity)
| ~ spl0_12 ),
inference(superposition,[],[f12733,f11116]) ).
fof(f13664,plain,
( spl0_14
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f11207,f11114,f13658]) ).
fof(f11207,plain,
( identity = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity)
| ~ spl0_12 ),
inference(forward_demodulation,[],[f11196,f9]) ).
fof(f11196,plain,
( greatest_lower_bound(identity,identity) = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity)
| ~ spl0_12 ),
inference(superposition,[],[f1799,f11116]) ).
fof(f13663,plain,
( spl0_14
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f11201,f11114,f13658]) ).
fof(f11201,plain,
( identity = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity)
| ~ spl0_12 ),
inference(forward_demodulation,[],[f11170,f1]) ).
fof(f11170,plain,
( multiply(identity,identity) = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity)
| ~ spl0_12 ),
inference(superposition,[],[f6232,f11116]) ).
fof(f13662,plain,
( spl0_14
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f11200,f11114,f13658]) ).
fof(f11200,plain,
( identity = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity)
| ~ spl0_12 ),
inference(forward_demodulation,[],[f11169,f9]) ).
fof(f11169,plain,
( greatest_lower_bound(identity,identity) = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity)
| ~ spl0_12 ),
inference(superposition,[],[f6352,f11116]) ).
fof(f13661,plain,
( spl0_14
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f11189,f11114,f13658]) ).
fof(f11189,plain,
( identity = greatest_lower_bound(inverse(multiply(inverse(a),b)),identity)
| ~ spl0_12 ),
inference(superposition,[],[f138,f11116]) ).
fof(f11218,plain,
( spl0_13
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f11166,f11109,f11210]) ).
fof(f11210,plain,
( spl0_13
<=> identity = least_upper_bound(inverse(multiply(inverse(b),a)),identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f11109,plain,
( spl0_11
<=> identity = least_upper_bound(identity,inverse(multiply(inverse(b),a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f11166,plain,
( identity = least_upper_bound(inverse(multiply(inverse(b),a)),identity)
| ~ spl0_11 ),
inference(forward_demodulation,[],[f11152,f8]) ).
fof(f11152,plain,
( least_upper_bound(identity,identity) = least_upper_bound(inverse(multiply(inverse(b),a)),identity)
| ~ spl0_11 ),
inference(superposition,[],[f9705,f11111]) ).
fof(f11111,plain,
( identity = least_upper_bound(identity,inverse(multiply(inverse(b),a)))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f11109]) ).
fof(f11217,plain,
( spl0_13
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f11165,f11109,f11210]) ).
fof(f11165,plain,
( identity = least_upper_bound(inverse(multiply(inverse(b),a)),identity)
| ~ spl0_11 ),
inference(forward_demodulation,[],[f11151,f1]) ).
fof(f11151,plain,
( multiply(identity,identity) = least_upper_bound(inverse(multiply(inverse(b),a)),identity)
| ~ spl0_11 ),
inference(superposition,[],[f9560,f11111]) ).
fof(f11216,plain,
( spl0_13
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f11163,f11109,f11210]) ).
fof(f11163,plain,
( identity = least_upper_bound(inverse(multiply(inverse(b),a)),identity)
| ~ spl0_11 ),
inference(forward_demodulation,[],[f11148,f8]) ).
fof(f11148,plain,
( least_upper_bound(identity,identity) = least_upper_bound(inverse(multiply(inverse(b),a)),identity)
| ~ spl0_11 ),
inference(superposition,[],[f3751,f11111]) ).
fof(f11215,plain,
( spl0_13
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f11156,f11109,f11210]) ).
fof(f11156,plain,
( identity = least_upper_bound(inverse(multiply(inverse(b),a)),identity)
| ~ spl0_11 ),
inference(forward_demodulation,[],[f11121,f1]) ).
fof(f11121,plain,
( multiply(identity,identity) = least_upper_bound(inverse(multiply(inverse(b),a)),identity)
| ~ spl0_11 ),
inference(superposition,[],[f5460,f11111]) ).
fof(f11214,plain,
( spl0_13
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f11155,f11109,f11210]) ).
fof(f11155,plain,
( identity = least_upper_bound(inverse(multiply(inverse(b),a)),identity)
| ~ spl0_11 ),
inference(forward_demodulation,[],[f11120,f8]) ).
fof(f11120,plain,
( least_upper_bound(identity,identity) = least_upper_bound(inverse(multiply(inverse(b),a)),identity)
| ~ spl0_11 ),
inference(superposition,[],[f5518,f11111]) ).
fof(f11213,plain,
( spl0_13
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f11141,f11109,f11210]) ).
fof(f11141,plain,
( identity = least_upper_bound(inverse(multiply(inverse(b),a)),identity)
| ~ spl0_11 ),
inference(superposition,[],[f252,f11111]) ).
fof(f11117,plain,
( spl0_12
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f11106,f11047,f11114]) ).
fof(f11047,plain,
( spl0_10
<=> identity = least_upper_bound(multiply(inverse(a),b),identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f11106,plain,
( identity = greatest_lower_bound(identity,inverse(multiply(inverse(a),b)))
| ~ spl0_10 ),
inference(forward_demodulation,[],[f11091,f336]) ).
fof(f11091,plain,
( identity = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(a),b)),identity))
| ~ spl0_10 ),
inference(superposition,[],[f9043,f11049]) ).
fof(f11049,plain,
( identity = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f11047]) ).
fof(f9043,plain,
! [X22,X23] : identity = greatest_lower_bound(identity,multiply(inverse(X22),least_upper_bound(X22,X23))),
inference(superposition,[],[f11,f348]) ).
fof(f11112,plain,
( spl0_11
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f10965,f10797,f11109]) ).
fof(f10797,plain,
( spl0_8
<=> identity = greatest_lower_bound(multiply(inverse(b),a),identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f10965,plain,
( identity = least_upper_bound(identity,inverse(multiply(inverse(b),a)))
| ~ spl0_8 ),
inference(forward_demodulation,[],[f10873,f336]) ).
fof(f10873,plain,
( identity = least_upper_bound(identity,multiply(inverse(multiply(inverse(b),a)),identity))
| ~ spl0_8 ),
inference(superposition,[],[f9068,f10799]) ).
fof(f10799,plain,
( identity = greatest_lower_bound(multiply(inverse(b),a),identity)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f10797]) ).
fof(f9068,plain,
! [X11,X12] : identity = least_upper_bound(identity,multiply(inverse(X11),greatest_lower_bound(X11,X12))),
inference(forward_demodulation,[],[f8964,f2]) ).
fof(f8964,plain,
! [X11,X12] : multiply(inverse(X11),X11) = least_upper_bound(identity,multiply(inverse(X11),greatest_lower_bound(X11,X12))),
inference(superposition,[],[f348,f10]) ).
fof(f11055,plain,
( spl0_10
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f11045,f10995,f11047]) ).
fof(f10995,plain,
( spl0_9
<=> identity = least_upper_bound(identity,multiply(inverse(a),b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f11045,plain,
( identity = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f11032,f8]) ).
fof(f11032,plain,
( least_upper_bound(identity,identity) = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_9 ),
inference(superposition,[],[f9705,f10997]) ).
fof(f10997,plain,
( identity = least_upper_bound(identity,multiply(inverse(a),b))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f10995]) ).
fof(f11054,plain,
( spl0_10
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f11044,f10995,f11047]) ).
fof(f11044,plain,
( identity = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f11031,f1]) ).
fof(f11031,plain,
( multiply(identity,identity) = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_9 ),
inference(superposition,[],[f9560,f10997]) ).
fof(f11053,plain,
( spl0_10
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f11042,f10995,f11047]) ).
fof(f11042,plain,
( identity = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f11028,f8]) ).
fof(f11028,plain,
( least_upper_bound(identity,identity) = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_9 ),
inference(superposition,[],[f3751,f10997]) ).
fof(f11052,plain,
( spl0_10
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f11036,f10995,f11047]) ).
fof(f11036,plain,
( identity = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f11002,f1]) ).
fof(f11002,plain,
( multiply(identity,identity) = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_9 ),
inference(superposition,[],[f5460,f10997]) ).
fof(f11051,plain,
( spl0_10
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f11035,f10995,f11047]) ).
fof(f11035,plain,
( identity = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f11001,f8]) ).
fof(f11001,plain,
( least_upper_bound(identity,identity) = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_9 ),
inference(superposition,[],[f5518,f10997]) ).
fof(f11050,plain,
( spl0_10
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f11021,f10995,f11047]) ).
fof(f11021,plain,
( identity = least_upper_bound(multiply(inverse(a),b),identity)
| ~ spl0_9 ),
inference(superposition,[],[f252,f10997]) ).
fof(f10998,plain,
( spl0_9
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f10900,f68,f10995]) ).
fof(f10900,plain,
( identity = least_upper_bound(identity,multiply(inverse(a),b))
| ~ spl0_4 ),
inference(superposition,[],[f9068,f70]) ).
fof(f10803,plain,
( spl0_8
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f10795,f10758,f10797]) ).
fof(f10758,plain,
( spl0_7
<=> identity = greatest_lower_bound(identity,multiply(inverse(b),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f10795,plain,
( identity = greatest_lower_bound(multiply(inverse(b),a),identity)
| ~ spl0_7 ),
inference(forward_demodulation,[],[f10788,f9]) ).
fof(f10788,plain,
( greatest_lower_bound(identity,identity) = greatest_lower_bound(multiply(inverse(b),a),identity)
| ~ spl0_7 ),
inference(superposition,[],[f1799,f10760]) ).
fof(f10760,plain,
( identity = greatest_lower_bound(identity,multiply(inverse(b),a))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f10758]) ).
fof(f10802,plain,
( spl0_8
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f10790,f10758,f10797]) ).
fof(f10790,plain,
( identity = greatest_lower_bound(multiply(inverse(b),a),identity)
| ~ spl0_7 ),
inference(forward_demodulation,[],[f10763,f1]) ).
fof(f10763,plain,
( multiply(identity,identity) = greatest_lower_bound(multiply(inverse(b),a),identity)
| ~ spl0_7 ),
inference(superposition,[],[f6232,f10760]) ).
fof(f10801,plain,
( spl0_8
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f10789,f10758,f10797]) ).
fof(f10789,plain,
( identity = greatest_lower_bound(multiply(inverse(b),a),identity)
| ~ spl0_7 ),
inference(forward_demodulation,[],[f10762,f9]) ).
fof(f10762,plain,
( greatest_lower_bound(identity,identity) = greatest_lower_bound(multiply(inverse(b),a),identity)
| ~ spl0_7 ),
inference(superposition,[],[f6352,f10760]) ).
fof(f10800,plain,
( spl0_8
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f10781,f10758,f10797]) ).
fof(f10781,plain,
( identity = greatest_lower_bound(multiply(inverse(b),a),identity)
| ~ spl0_7 ),
inference(superposition,[],[f138,f10760]) ).
fof(f10761,plain,
( spl0_7
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f10689,f883,f10758]) ).
fof(f10689,plain,
( identity = greatest_lower_bound(identity,multiply(inverse(b),a))
| ~ spl0_6 ),
inference(superposition,[],[f9043,f885]) ).
fof(f946,plain,
( spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f881,f19,f883]) ).
fof(f19,plain,
( spl0_1
<=> a = least_upper_bound(a,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f881,plain,
( a = least_upper_bound(b,a)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f876,f8]) ).
fof(f876,plain,
( least_upper_bound(b,a) = least_upper_bound(a,a)
| ~ spl0_1 ),
inference(superposition,[],[f188,f252]) ).
fof(f188,plain,
( ! [X0] : least_upper_bound(a,least_upper_bound(b,X0)) = least_upper_bound(a,X0)
| ~ spl0_1 ),
inference(superposition,[],[f7,f21]) ).
fof(f21,plain,
( a = least_upper_bound(a,b)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f945,plain,
( spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f879,f19,f883]) ).
fof(f879,plain,
( a = least_upper_bound(b,a)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f864,f8]) ).
fof(f864,plain,
( least_upper_bound(b,a) = least_upper_bound(a,a)
| ~ spl0_1 ),
inference(superposition,[],[f252,f188]) ).
fof(f886,plain,
( spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f858,f19,f883]) ).
fof(f858,plain,
( a = least_upper_bound(b,a)
| ~ spl0_1 ),
inference(superposition,[],[f252,f21]) ).
fof(f123,plain,
spl0_5,
inference(avatar_split_clause,[],[f114,f119]) ).
fof(f119,plain,
( spl0_5
<=> identity = inverse(identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f114,plain,
identity = inverse(identity),
inference(superposition,[],[f2,f106]) ).
fof(f106,plain,
! [X0] : multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[],[f45,f77]) ).
fof(f122,plain,
spl0_5,
inference(avatar_split_clause,[],[f112,f119]) ).
fof(f112,plain,
identity = inverse(identity),
inference(superposition,[],[f106,f2]) ).
fof(f74,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f66,f57,f68]) ).
fof(f57,plain,
( spl0_3
<=> b = greatest_lower_bound(b,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f66,plain,
( b = greatest_lower_bound(a,b)
| ~ spl0_3 ),
inference(superposition,[],[f4,f59]) ).
fof(f59,plain,
( b = greatest_lower_bound(b,a)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f73,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f65,f57,f68]) ).
fof(f65,plain,
( b = greatest_lower_bound(a,b)
| ~ spl0_3 ),
inference(superposition,[],[f4,f59]) ).
fof(f72,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f62,f57,f68]) ).
fof(f62,plain,
( b = greatest_lower_bound(a,b)
| ~ spl0_3 ),
inference(superposition,[],[f59,f4]) ).
fof(f71,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f61,f57,f68]) ).
fof(f61,plain,
( b = greatest_lower_bound(a,b)
| ~ spl0_3 ),
inference(superposition,[],[f59,f4]) ).
fof(f60,plain,
( spl0_3
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f48,f19,f57]) ).
fof(f48,plain,
( b = greatest_lower_bound(b,a)
| ~ spl0_1 ),
inference(superposition,[],[f33,f21]) ).
fof(f27,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f17,f24]) ).
fof(f17,axiom,
inverse(b) != least_upper_bound(inverse(a),inverse(b)),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',prove_p39a) ).
fof(f22,plain,
spl0_1,
inference(avatar_split_clause,[],[f16,f19]) ).
fof(f16,axiom,
a = least_upper_bound(a,b),
file('/export/starexec/sandbox/tmp/tmp.q0O5Q55OwC/Vampire---4.8_1434',p39a_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : GRP190-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.34 % Computer : n010.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Wed Aug 30 17:14:33 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.19/0.40 % (1567)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.41 % (1572)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.19/0.41 % (1575)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.19/0.41 % (1574)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.19/0.41 % (1580)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.19/0.41 % (1578)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.19/0.41 % (1582)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.19/0.41 TRYING [1]
% 0.19/0.41 % (1571)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.19/0.41 TRYING [2]
% 0.19/0.41 TRYING [3]
% 0.19/0.42 TRYING [1]
% 0.19/0.42 TRYING [2]
% 0.19/0.43 TRYING [4]
% 0.19/0.43 TRYING [3]
% 0.19/0.47 TRYING [4]
% 0.19/0.48 TRYING [5]
% 0.19/0.60 TRYING [5]
% 1.28/0.68 TRYING [6]
% 4.02/0.99 TRYING [6]
% 5.62/1.27 TRYING [7]
% 7.41/1.51 TRYING [1]
% 7.41/1.51 TRYING [2]
% 7.41/1.51 TRYING [3]
% 7.41/1.53 TRYING [4]
% 8.40/1.59 TRYING [5]
% 10.47/1.89 TRYING [6]
% 12.71/2.23 TRYING [7]
% 17.42/2.90 TRYING [8]
% 18.76/3.10 TRYING [7]
% 36.66/5.67 % (1574)First to succeed.
% 36.66/5.68 % (1574)Refutation found. Thanks to Tanya!
% 36.66/5.68 % SZS status Unsatisfiable for Vampire---4
% 36.66/5.68 % SZS output start Proof for Vampire---4
% See solution above
% 36.66/5.68 % (1574)------------------------------
% 36.66/5.68 % (1574)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 36.66/5.68 % (1574)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 36.66/5.68 % (1574)Termination reason: Refutation
% 36.66/5.68
% 36.66/5.68 % (1574)Memory used [KB]: 64732
% 36.66/5.68 % (1574)Time elapsed: 5.250 s
% 36.66/5.68 % (1574)------------------------------
% 36.66/5.68 % (1574)------------------------------
% 36.66/5.68 % (1567)Success in time 5.317 s
% 36.66/5.68 % Vampire---4.8 exiting
%------------------------------------------------------------------------------